Handelshochschule Leipzig (HHL)
Logic, Game Theory, and the Real World
Arnis Vilks
HHL - Arbeitspapier Nr. 73
Copyright:2006
Jede Form der Weitergabe und Vervielfältigung
bedarf der Genehmigung des Herausgebers
Logic, Game Theory, and the Real World
Arnis Vilks 1
Leipzig Graduate School of Management (HHL)
[email protected]
Introduction
Both Logic and Game Theory are fascinating fields. I for one have always been
intrigued by the perennial philosophical puzzle of how reasoning works and
which kind of reasoning is sound. How reasoning human agents interact with
each other, and how they contribute to each other’s well-being, and why they
often harm each other, is a similar perennial puzzle, but for some reason its
more explicit investigation has had to wait for the genius of John von Neumann.
I am quite confident, however, that in the history of thought bright men or
women before von Neumann must have thought about the “I think that you think
that he thinks that I think”-loops that are so typical for game theoretic reasoning.
In fact, this little observation about game-theoretic reasoning already makes
clear why game theory cannot really live without including logic into its field of
inquiry.
Many years ago, when I was a student at Hamburg University, I was taught that
Logic is the theory of valid or correct reasoning. One might perhaps use
“rational” as opposed to factual reasoning as a third near-synonym. My logic
professors some 30 years ago made much of the point that logic is not
psychology. The latter may try to investigate how people actually develop, i.e.,
modify and extend their belief systems, even if no external information arrives.
That is, psychology may look at how people actually think. But Logic, I was told,
is rather a normative discipline. It tells you, how you ideally ought to reason,
what you are allowed or required to infer from given premises. Thus, it seems
that Logic needs to prove that the inferences it singles out as correct, cannot
lead you astray. As – I assume - many other serious students of logic, I was
somewhat puzzled by the fact that in proving the theorems of logic one
frequently makes use of just those very modes of reasoning the validity of which
one is proving - but of course the distinction between formal and informal proofs,
between object- and metalanguage made that puzzle much less worrying.
Some years later, I was taught, and many economics students all over the world
are still taught today, that Game Theory studies the interaction of rational
agents, where “rationality” has a double meaning. It covers both rationality of
choice, and rationality of reasoning. Rationality of choice means that relative to
the information you happen to have, you choose what you prefer most among
the options you consider possible. If I observe you sitting and listening, I may
thus infer by the rationality of choice principle that, however annoyed you may
1
This paper, presented at the opening ceremony of GloriClass, was written while I was visiting Waikato
Management School in Hamilton, New Zealand, in the first months of 2006.
3
be by what I am saying, your observable choice reveals that right now you
prefer sitting and listening to getting up and leaving. In making this inference, I
certainly take for granted that you consider it possible to leave, but given this
assumption, observed behaviour implies certain things about preferences.
The second part of Game Theory’s standard rationality assumption is more or
less just the assumption that the players’ reasoning is correct, and that no
relevant inference fails to be made. This is sometimes expressed by saying that
game theory assumes players to be perfect logicians. Actually, they are often
required not only to be logicians, but to know a good deal about higher layers of
mathematics as well, but most game theorists don’t know much about the
distinction between logic and mathematics.
Now, unlike the rationality of choice principle, logical omniscience seems a
pretty bold assumption to make. After all, game theory is meant to elucidate
actual behaviour of human beings in situations where they interact, and actually
reason about each others’ reasoning.
This brings me closer to one of the main points I would like to make. Game
theory has become the most important tool kit for economists, and it is
sometimes also used in political science, because it seems to elucidate realworld interactions. The world is of course full of interaction between humans.
Every organisation or institution is brimming with interaction, every market is
essentially interaction, not to mention international politics like the current scary
escalation of violence between Islamic extremists and the George-W.-Bush-led
Western alliances.
Of course, as most of you know, game theory can also be applied to the
interaction of machines and software agents, and John Maynard Smith has
inspired the development of a whole new sub-discipline - evolutionary game
theory - by showing that many game theoretic ideas can be applied to the
interaction of animals – without of course assuming them to be perfect
mathematicians. Unlike its rationalistic ancestor, evolutionary game theory does
not look at interaction between a few, who consciously choose their respective
strategies, but it looks at whole populations of agents who are genetically
programmed to play particular strategies, and who may or may not have
offspring with the same genes – depending on how “fit” their strategy makes
them to survive within the current population’s “mix” of strategies.
Of course, with certain modifications and reinterpretations, this non-rationalistic
branch of game theory can also be applied to the interaction among populations
of machines or computer programmes – and it can also be applied to that
particular species of animal that likes to think of itself as very different from all
other species, because it has free will to choose and because it a mind to
reason.
I am getting even closer to the point I want to make. There are conflicts and
interactions between humans in the real world out there that arguably cost
many thousands of human lives each day. Nevertheless, the reasoning that
4
apparently informs the most far-reaching strategic decisions of the political and
business leaders in the real world, appears to be often so innocent of any
decision-theoretic or game-theoretic wisdom that one cannot but marvel at the
lack of interaction between us thinkers, and those who move and often shake
the world.
Now, it is always easy to blame others, and intellectuals tend to underestimate
the amount and complexity of reasoning that quite a few of the people in
authority, actually do carry out before making their strategic choices. But if I am
right that many important decisions “out there” lack all the insights that logic and
game theory can provide, I think we intellectuals have to blame ourselves, too. I
have the impression that both fields we are talking about today, both logic and
game theory, often tend to ignore the important problems, and waste much time
and effort in defining precisely, and then solving problems - which nobody had
before they were invented by the logicians or game theorists.
Even the terminologies used within our fields tend to be so idiosyncratic that
members of one research group sometimes have great difficulties to even
understand what is written by a member of another research group.
Now, I am not, of course, urging the Amsterdam GloriClass to forego research
on foundational issues, or to write popular expositions of logic and game theory
for the politician. Actually, I try not to urge anybody to do anything. But I kindly
invite you to consider the research you are doing in the context of the problems
out there which urgently await if not solutions then at least informed advice on
the soundness of reasoning and on the rationality of choice.
A simple game of some importance
To illustrate, let me consider a very simple example. Assume there are two
players, the rich civilization R, and the poor one P. Both have two strategies: To
play “aggressive” A, or to play “meek” M. If both play meek, the rich civilization
gets almost the whole “pie”, which I take to be 22 t USD, but the poor can
improve a little against this allocation by playing aggressive. If the rich play
aggressive they hurt the poor, but against a meek strategy by the poor, the rich
loose only little. If both play aggressive – well, humankind may not survive the
ensuing nuclear war.
A first distinction can be illustrated here, the one between decision-theoretic
rationality and game-theoretic rationality. While it is clearly the dominant
strategy for the rich to play meek, the poor civilization’s best response depends
on its opponent’s choice. If the poor do not know about the character of the rich,
and therefore regard both strategies of the rich as equiprobable, the poor will be
indifferent between its two strategies, and hence may well choose to play meek.
Many other beliefs of the poor, represented by a probability distribution over its
opponent’s strategies, are of course just as consistent with playing meek.
However, considering that the rich opponent is rational, and knowing about the
structure of the game, the poor must conclude that the rich will not play
5
aggressive, but meek. Therefore game theory recommends the aggressive
strategy to the poor.
P
R
A
M
0
A
1
0
18
3
M
17
2
20
Obviously, the strategy combination (M,A), where the first component denotes
the rich player’s strategy, is the only Nash equilibrium for this little game, and
one might think this all one can say.
Not so. Do you really think (M,A) is rational? As I just mentioned, there are
different notions of rationality. Decision-theoretic rationality does not quite
coincide with game-theoretic rationality. One is more “demanding” than the
other, but both are treated as normative concepts in the sense I indicated by
saying that game theory “recommends” M to R and A to P.
But the more thoughtful game-theorists such as Harsanyi have been very aware
of the fact that there is of course a still more demanding notion of rationality –
what one may call moral, ethical, or fully normative rationality. Assume for a
moment that both civilizations have the same number of people, and that each
poor life counts just as much as a rich one. Is there an outcome that is ethically
rational? You think ethics is neither logic nor game-theory? But as long as both
disciplines end up making recommendations, and tell you what you should infer
from given premises, and what the rational strategy choice is, both disciplines
are normative. So why stop at the conventional wisdom of a Nash equilibrium?
You may say, none of the outcomes looks particularly “ethical”.
Right, I agree. So, what about inventing a new strategy, call it the innovative
one.
P
R
A
M
0
A
0
M
17
I
17
1
18
3
2
20
3
11
11
6
You might say, well that’s a different game. Of course it is. Within the academic
world of the game theorist, it may be considered “cheating” if, in the middle of
an analysis, you all of a sudden “add” a new strategy.
But imagine we are modelling a real world conflict. How do we know which
strategies are “available”? What does it mean to claim that a real human in a
particular situation has options A, B, C and no others? Both George W. Bush
and Usama bin Laden may have thought that, in order to achieve their
respective goals, they had no better option but to ask their followers to go to
faraway countries, and to kill themselves and many others. But maybe they
were just lacking creativity. I think it is a very relevant (and essentially open)
question of logic in game theory what we take an “option” to be.
(I do think it is easier to see the problem in the context of a serious application
than in an Alice-and-Bob-type toy example, but I did not necessarily mean to
suggest that my model of the “clash of civilizations” is capturing all the
essentials of that global problem. There is a folk meta-theorem of gametheoretic modelling to the effect that for any given result there is a set of gametheoretic assumptions from which the result follows. It goes without saying that
if I had wanted to praise the US president here, I could have designed a
different little game than the one I just presented – a game which would yield
what I wanted to show: Not invading Iraq must lead to disaster.)
Eight important logical problems of game theory
I guess I have messed up things a little. So let me try to disentangle some of the
logical problems of game theory which I see as really important. I will briefly
explain eight such issues.
1. The distinction between a normative and a predictive (or descriptive) use of
theory is of utmost importance in applications of game theory. Are the solutions
we define in game theory what we ought to recommend? Or are they just some
kind of “predictions”? Maybe this is more of a philosophical or methodological
issue than a logical one, but it seems to be also very relevant to logic itself. I do
not have to tell you about the plethora of logical systems which have been
analysed in the learned monographs and journals. If that is not just playing
around with symbols, than what is the status of those systems? “Should” we
use classical or intuitionistic logic when we reason about games? Should we
use a different one when we reason about quantum information? A Leipzig
colleague of mine, Piero La Mura has recently generalized Aumann’s concept of
correlated equilibrium to allow for correlation by means of possibly entangled qbits. Which logic should we use in reasoning about this? To ask the question
again: what is the logical status of Logic and of GT? Normative, predictive, or
what? Johan van Bentham has recently written that “discussions of ‘normative’
versus ‘predictive’ views of logic have become predictable and boring”. That
may be so, but it is an issue which is can hardly be avoided unless one is happy
to confine oneself to the narrow world of “pure”, academic, discourse. To my
mind, game theory today should help to avoid World War III.
7
2. Of course one of the strategies academics use in order to answer a question
consists of making distinctions. Of course one can begin to define normativity1
as opposed to normativity2 as distinct from rationality 4. I know full well, of
course, that one often needs to make the right distinctions, if one wants to
convince others. But even more important than making clever distinctions, and
leave it at that, is to make a difference. I very much hope, and I trust, that the
research that is going to be done in the GloriClass is going to make a difference,
but if it made a difference not only to some other members of GloriClass, that
would be splendid. In the world of Business today, where game theory is used
and applied, the importance of ethics is widely acknowledged. Scandalous
behaviour by Top-Managers as exemplified by, e.g., the Enron and Worldcom
cases, may have been the main reason for this, but the fact remains that
Business Ethics is increasingly seen as necessary by quite sober-minded
business people. There are of course applications of logic to ethics and law,
which might well be reconsidered in the context of games. Or to put this as a
question: What is the logic of “fully normative” or “ethical” recommendations?
3. More specifically, the logical relation between standard game-theoretic
rationality and whatever one takes ethical rationality to be, needs to be
addressed. Just as game-theoretic rationality is a special case of decisiontheoretic rationality, one would expect moral or ethical rationality to be a special
case of game-theoretic rationality. But look at my 3*2 example again. You may
have noticed that inventing the innovative strategy did not really help at first
glance. The extended game still has just one Nash equilibrium – the one we
had before. Can we expect anything else than (M,A) in the extended game?
Maybe not, if game theory is interpreted as predictive, but if the model was used
in normative sense, one might - perhaps - think up and defend an ethical
justification for the outcome (11,11). Should we then recommend I to R, rather
than M? As far as I am aware, such questions are not among the “standard”
questions logicians are trained to think about. But who else if not logicians - or
maybe philosophers with a good understanding of logic and game-theory should be able to address them?
4. The notion of an option or “feasible choice” that is presupposed by game
theory has puzzled me a lot. I made a suggestion before my 5-year excursion
into the world of business to the effect that one can interpret the “dual” of the
epistemic-logic “knowledge” operator, ¬K¬, to express what a player
subjectively “considers possible”. I still think that was a good idea. But when I
presented it at a LOFT conference with Bob Aumann in the audience, he almost
got angry with me, and repeated a couple of times that the “feasible” actions in
a game are not those whereof one does not yet know that one will not carry
them out. With his amazing mathematical intuition he had apparently deduced
on the spot that all “real” decision problems would be reduced to trivial ones
within his preferred framework of S5. The situation is quite close to the one in
Fitch’s paradox: If it is the case that I will choose M, but still consider it possible
that I will not choose M, one would like it to be possible to know this. In one of
those most useful coffee breaks after my talk, Aumann very kindly approached
me to say he was sorry about getting angry, and explained that he thought the
feasible options in a game must be the objectively given, physically possible
8
actions. Well, I like and respect Bob Aumann very much, he no doubt deserved
the Nobel prize he got last year, but I find the idea that the feasible moves in a
game are all the physically possible ones, outright grotesque. We never know
all the physically possible actions we might carry out at any given instant, and if
we did, and moreover could somehow “specify” all of them, there would just be
one big “game of life” – or Savage’s “grand world decision problem” - left to
consider, and any attempt to “apply” the tiny little textbook games we think are
useful to analyse real-world conflicts and cooperation would at best be reduced
to training material for students. So I challenge you logicians to think about what
exactly turns a hypothetical action into one that has to be included as a move in
the relevant game.
5. There is another problem that links game theory with logic. It is the problem
of choosing the optimal logic. To take just epistemic logic as an example, most
of you know that one can define somewhat different systems even within the
narrow confines of Kripkean, or, say, neighbourhood, semantics. There are the
systems K, KT, S4, S5, and many others. Of course, in a relaxed research
environment there may be little need to “choose” one instead of the others. But
in applications one would very much want to know which model of knowledge is
the most appropriate one. In principle, decision or game theory should be able
at least to give structure to the problem of rational choice between alternative
“logical” options. But again - the devil is in the detail, and as soon as one looks
closely at the basics of decision theory, the dividing line between logic and
decision theory seems elusive. I mentioned the principle of rational choice in my
introductory remarks. Let me repeat what it says. “If one chooses an action, it
must have been considered feasible by the agent, and there cannot be another
feasible one that is preferred to the chosen one.” Depending, of course, on a
number of details about the notions of action and preference, non-logicians
have criticized this principle of rational choice as an “empty tautology”. At least
on a slightly naïve account of logic, it seems “logically impossible” to
simultaneously claim that a certain behaviour is an intentionally chosen action,
and that in the very moment of choosing this action - the chooser considers an
alternative action feasible which he actually prefers to the chosen one. So is
there a logic that connects actions, preference, and feasibility in such a way that
the principle is valid? If so, there might be a grand unified theory of logic and
games.
6. The next issue, I would like to mention, is the notion of “information”, and its
relation to the foundations of mathematics. Johan van Bentham has, I think
quite rightly, emphasized that the notion of information may be a more basic
notion for an adequate understanding of the world than the notions we have
inherited from the logicians of 100 years ago. It may well be that I am just
revealing my ignorance here, but I have not seen any theory of information that
could aspire to be the foundation for, say, most of the mathematics applied in
the sciences. I think it is fair to say that most applications of mathematics today
take it for granted that mathematics rests on a fairly safe basis, and that this
basis is the one thought up by Zermelo and Fraenkel, and later shown by the
Bourbaki group to produce virtually all of known useful mathematics. If one asks
why this basis is pretty safe, one can probably just point to the fact that the
9
mathematics that can be derived from it, has not only proved very useful in
combination with all sorts of non-mathematical ideas, but it has apparently
nowhere collided with observations or ideas which could claim to be just as
“evident” as the axioms of Zermelo-Fraenkel set theory. Now, you are probably
familiar with the Quine-Duhem thesis, which roughly says that one can “refute
by observation” only the conceptual apparatus used “as a whole”, but hardly
ever a particular segment of that conceptual apparatus. Thus, it is essentially a
matter of convention what is taken to be the infallible “hard core” of ones world
view. It seems clear to me that taking set theory to be “beyond reasonable
doubt” is such a convention. And conventions can and should be modified, if
there are convincing alternatives one can choose - and good reasons to actually
do choose some modification.
Now, again, I may just be revealing my personal ignorance when I say I have
not seen an alternative to standard set theory that could at least plausibly hold
the promise to clear away some of the conceptual riddles in fields like logic and
game theory - where in spite of the aforementioned zoo of logical systems, at
the meta-level standard mathematical logic and set theory are treated almost as
god-given. But there are such riddles, and somehow many of them seem to
confirm that information is more basic than sets. Let me mention one from a
field I know very little about, and explain another one that I know much better.
6.1. The field I know next to nothing about except that it seems to rely heavily
on the right way of modelling information, is quantum mechanics. Recently,
Conway and Kochen have discovered and proved a theorem that goes by the
name of “free-will theorem”. It says, apparently, that if an experimenter has
some free will, sub-atomic particles also have some free will. One of the
assumptions in the theorem is that there is a finite upper bound on the speed
with which information can be transmitted. Although the speed of light seems a
natural candidate for this upper bound, it seems that it is experimentally not that
clear that nothing can travel faster than light. And what is there in the theory of
information that tells us what the carrier of information must be? Is it absurd to
say that I sometimes transmit information to myself? Is the speed of thought
limited by the speed of light? Can we choose what to think next? Can we
choose to focus on one thought, and suppress any new ideas for a while? The
famous physicist Roger Penrose has argued forcefully that human thought is
creative and therefore not algorithmic. But as far as I know, the “physics of
mind” is still unknown.
6.2. There is another conceptual riddle that I am quite sure has not been
answered in the learned literature. To me, it strongly suggests that the logical
foundations of mathematics need modification if we want a satisfactory theory of
reasoning about choice. Imagine one of the simplest games there is – a oneplayer game with two strategies. Assume the strategies are actually given by
their payoffs. Let these be monetary payoffs, and assume our agent prefers
more to less money. Now, he is offered the choice between alternative payoffs
which would be given to him as gifts. Either he can have 37 or 74. Our agent,
like most of us, gets out his pocket calculator, types in the required calculations,
and ends up with the information 37 = 2187 and 74 = 2101. According to the
10
principle of rational choice, he chooses 37 instead of 74. So far, so good. What I
need to tell you, perhaps, is that I cheated again. Actually, 74=2401. The
situation I had in mind is one where our agent is unaware of the fact that his
pocket calculator has a defect. As it happens, the third digit from the right is
always a “1”. Now why is this a conceptual riddle? Well, standard predicate
logic with equality has the “axiom of substitutivity”, or “indiscernablility of
identicals” which says
Y=X → (P(Y)→P(X))
for any predicate P. Now let P(X) be the predicate “the agent has the
information that 2187>X”. As I assumed in my little fictitious story, P(74) is true.
It is also true that 74 = 2401. The axiom thus allows us to deduce P(2401). But it
seems plausible to assume that our fictitious agent is neither an idiot nor
otherwise out of his mind, and that P(2401) is false. It seems that if we did not
choose by convention to treat standard mathematical logic as irrefutable, we
would have a nice Popperian falsification of a logical axiom here.
7. I do not know, of course, how to deal satisfactorily with these and the many
other problems that arise in thinking about speed of thought, choice, free will, or
the so-called “propositional attitudes”. It is certainly easy to think up an ad-hoc
logic that allows one to accommodate any one of these problems. But one
certainly does not want to throw away the beloved, and essentially healthy,
baby of mathematics with the bathwater of some stubborn anomalies. What
seems needed is a theory - or logic - of information that is in accordance with
our intuitions and observations about the nature of information, but which can
still accommodate at least large parts of present-day mathematics. The
problems of information, consciousness, free will, and choice seem to be so
much at the intersection of quantum physics, logic, and decision theory that I for
one would not be overly surprised if the next big step in the history of thought
arose from a unified perspective on information and on how it is processed by
the human mind.
I mentioned already that because of creativity, human thought is not algorithmic.
A fortiori, it is not isomorphic to a formal system, as this term is commonly
defined. It may well be that a suitable modification of the definition of “formal
system” will do the trick of understanding how the human mind works, and will
allow one to defend the correspondingly reinterpreted “strong AI” thesis. In
order to allow for creativity, one might try to investigate open systems instead of
the usual formal ones. What do I mean by an open system? Well, it might look
much like a standard formal system – except that neither the alphabet nor the
axioms are fixed once and for all. Thus, we might say, let O be a system which
has an alphabet a,b,c,…, and possibly also Greek, Arabic, Chinese, or still other
characters. These may be introduced if required, but not without giving reasons.
We might specify a certain number of assumptions or “axioms” and rules of
inference, but allow for other assumptions to be introduced if required – but
again not without mentioning that the formula or sentence written down is meant
to be a new, additional, assumption. There is, of course, a notion of derived or
inferred formula in O. A formula F is derived in O, if it is the last one of a finite
11
sequence such that each element of the sequence is either an assumption or
derived from previous elements. At any given moment, one can “freeze” an
open system into the formal one that has as its alphabet and axioms only the
signs and assumptions introduced so far. There may not be many other
interesting things one can say about all open systems. But are there many
interesting things one can say about all formal systems? In order to say
something interesting, one needs to get more specific, but the only point I want
to make here, is this: The notion of “formal system” is not one that cannot be
modified in interesting ways. Certainly, it seems quite straightforward to develop
standard mathematics within an open system – I cannot see that anything
would need to get lost. But of course, the associated philosophy of mathematics
would be closer to Lakatos’ Proofs and Refutations than to Bourbaki’s Théorie
des Ensembles.
One would hope that logic and mathematics are capable of progress, and
maybe the time is ripe for a step forward after 100 years of essentially refining
the received view of Frege, Russell, Zermelo and Fraenkel. Why not think
about how to do this big step in the Amsterdam GloriClass?
8. The eighth and last issue I would like to try and disentangle from the others
hidden in my little clash-of-civilizations game, probably needs to be addressed
jointly with the issue of what constitutes information. It is the issue of how one
interprets some given information. There is of course much learned literature
about both formal and informal semantics, but the basic idea seems to be that
any given information typically admits of different interpretations. I think I do not
overly stretch the ordinary usage of the English language when I say that the
information we have about the “clash” can be interpreted as an indication that if
the escalation continues, the American president may one day decide to
sacrifice the people who crucified Jesus. Both George W. Bush and Usama bin
Laden are known to interpret their respective holy books in a very literal - if not
naïve – way. One of the more obvious urgent things logicians should do, is
telling the world out there that for any given information or book, no fallible
human knows the only correct “reading” or interpretation.
Educated men and women should know that both the Bible and the Qu’ran have
content that cannot be interpreted “literally”, even if one tries. The very concept
of a God who is beyond human understanding makes the word “god” - a
metaphor.
Conclusion
Now it seems, I have “come full circle”, as they say. To conclude, I suggest that
logicians working on game theory should neither fall prey to the ever-present
temptation of misplaced modesty in the choice of topics and issues, nor
succumb to the pressure of publishing many instead of good papers. The LPU
or “least publishable unit” of wisdom – like other very small particles - may well
be subject to Heisenberg’s uncertainty principle: As soon as its content has
been “observed” by careful reading, it has already sped into the forgotten
prehistory of human thinking. And if you try to keep it in the present, its position
12
reduces to an item in your list of publications that is not read or understood by
anybody.
Wisdom and courage are virtues that must not be separated by the societal
division of labour – wisdom and cowardice for the scholars and academics, as it
were, and thoughtless bravery for those in authority. If nothing else, the need to
convince those who allocate research funds should make logic in game theory
be aware of how relevant both fields are, or at any rate how relevant both fields
might again become – relevant both to quite down-to-earth issues of economics
and international politics, and to seemingly remote academic disciplines like
quantum physics or theology.
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Harsanyi, J., Morality and the Theory of Rational Behaviour, in: Sen, A.
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Van Bentham, J., Where is Logic Going, and Should It? In: Bencivenga,
E. (ed.), What Is to Be Done in Philosophy?
Vilks, A., What is a Game? In: Bolle, F., and Carlberg, M. (eds.),
Advances in Behavioral Economics. Essays in Honor of Horst Todt.
Heidelberg: Physica, 2001.
Vilks, A., Rationality of Choice and Rationality of Reasoning, HHL
Working Paper, 1996.
13
Handelshochschule Leipzig (HHL)
Arbeitspapiere
Die Arbeitspapiere der Handelshochschule Leipzig (HHL) erscheinen in
unregelmäßigen Abständen. Bisher sind folgende Arbeiten erschienen:
Nr. 1
Prof. Dr. Dr. h.c. Heribert Meffert (1996), 31 Seiten
Stand und Perspektiven des Umweltmanagement in der
betriebswirtschaftlichen Forschung und Lehre
Nr. 2
Prof. Dr. Bernhard Schwetzler (1996), 28 Seiten
Verluste trotz steigender Kurse? - Probleme der
Performancemessung bei Zinsänderungen
Nr. 3
Prof. Dr. Arnis Vilks (1996), 26 Seiten
Rationality of Choice and Rationality of Reasoning (Revised
version, September 1996)
Nr. 4
Prof. Dr. Harald Hungenberg (1996), 36 Seiten
Strategische Allianzen im Telekommunikationsmarkt
Nr. 5
Prof. Dr. Bernhard Schwetzler (1996), 41 Seiten
Die Kapitalkosten von Rückstellungen zur Anwendung des
Shareholder Value-Konzeptes in Deutschland
Nr. 6
Prof. Dr. Harald Hungenberg / Thomas Hutzschenreuter (1997),
32 Seiten
Postreform - Umgestaltung des Post- und Telekommunikationssektors in Deutschland
Nr. 7
Prof. Dr. Harald Hungenberg / Thomas Hutzschenreuter /
Torsten Wulf (1997), 31 Seiten
Investitionsmanagement in internationalen Konzernen
- Lösungsansätze vor dem Hintergrund der Agency Theorie
Nr. 8
Dr. Peter Kesting (1997), 47 Seiten
Visionen, Revolutionen und klassische Situationen – Schumpeters
Theorie der wissenschaftlichen Entwicklung
Nr. 9
Prof. Dr. Arnis Vilks (1997), 36 Seiten
Knowledge of the Game, Rationality and Backwards Induction
14
Nr. 10
Prof. Dr. Harald Hungenberg / Thomas Hutzschenreuter /
Torsten Wulf (1997), 22 Seiten
Ressourcenorientierung und Organisation
Nr. 11
Prof. Dr. Bernhard Schwetzler / Stephan Mahn (1997),
71 Seiten
IPO´s: Optimale Preisstrategien für Emissionsbanken mit Hilfe von
Anbot-Modellen
Nr. 12
Prof. Dr. Thomas M. Fischer (1997), 23 Seiten
Koordination im Qualitätsmanagement – Analyse und Evaluation
im Kontext der Transaktionskostentheorie
Nr. 13
Dr. Thomas Hutzschenreuter / Alexander Sonntag (1998),
32 Seiten
Erklärungsansätze der Diversifikation von Unternehmen
Nr. 14
Prof. Dr. Bernhard Schwetzler / Niklas Darijtschuk (1998),
33 Seiten
Unternehmensbewertung mit Hilfe der DCF-Methode – eine
Anmerkung zum „Zirkularitätsproblem“
Nr. 15
Prof. Dr. Harald Hungenberg (1998), 22 Seiten
Kooperation und Konflikt aus Sicht der Unternehmensverfassung
Nr. 16
Prof. Dr. Thomas M. Fischer (1998), 31 Seiten
Prozesskostencontrolling – Gestaltungsoptionen in der
öffentlichen
Verwaltung
Nr. 17
Prof. Dr. Bernhard Schwetzler (1998), 34 Seiten
Shareholder Value Konzept, Managementanreize und
Stock Option Plans
Nr. 18
Prof. Dr. Bernhard Schwetzler / Serge Ragotzky (1998),
24 Seiten
Preisfindung und Vertragsbindungen bei MBO-Privatisierungen in
Sachsen
Nr. 19
Prof. Dr. Thomas M. Fischer / Dr. Jochen A. Schmitz (1998),
23 Seiten
Control Measures for Kaizen Costing - Formulation and Practical
Use of the Half-Life Model
Nr. 20
Prof. Dr. Thomas M. Fischer / Dr. Jochen A. Schmitz (1998),
35 Seiten
Kapitalmarktorientierte Steuerung von Projekten im Zielkostenmanagement
15
Nr. 21
Prof. Dr. Bernhard Schwetzler (1998), 25 Seiten
Unternehmensbewertung unter Unsicherheit –
Sicherheitsäquivalent- oder Risikozuschlagsmethode?
Nr. 22
Dr. Claudia Löhnig (1998), 21 Seiten
Industrial Production Structures and Convergence: Some Findings
from European Integration
Nr. 23
Peggy Kreller (1998), 54 Seiten
Empirische Untersuchung zur Einkaufsstättenwahl von
Konsumenten am Beispiel der Stadt Leipzig
Nr. 24
Niklas Darijtschuk (1998), 35 Seiten
Dividendenpolitik
Nr. 25
Prof. Dr. Arnis Vilks (1999), 25 Seiten
Knowledge of the Game, Relative Rationality, and Backwards
Induction without Counterfactuals
Nr. 26
Prof. Dr. Harald Hungenberg / Torsten Wulf (1999), 22 Seiten
The Transition Process in East Germany
Nr. 27
Prof. Dr. Thomas M. Fischer (2000), 28 Seiten
Economic Value Added (EVA®) - Informationen aus der externen
Rechnungslegung zur internen Unternehmenssteuerung?
(überarb. Version Juli 2000)
Nr. 28
Prof. Dr. Thomas M. Fischer / Tim von der Decken (1999),
32 Seiten
Kundenprofitabilitätsrechnung in Dienstleistungsgeschäften –
Konzeption und Umsetzung am Beispiel des Car Rental Business
Nr. 29
Prof. Dr. Bernhard Schwetzler (1999), 21 Seiten
Stochastische Verknüpfung und implizite bzw. maximal zulässige
Risikozuschläge bei der Unternehmensbewertung
Nr. 30
Prof. Dr. Dr. h.c. mult. Heribert Meffert (1999), 36 Seiten
Marketingwissenschaft im Wandel – Anmerkungen zur
Paradigmendiskussion
Nr. 31
Prof. Dr. Bernhard Schwetzler / Niklas Darijtschuk (1999),
20 Seiten
Unternehmensbewertung, Finanzierungspolitiken und optimale
Kapitalstruktur
Nr. 32
Prof. Dr. Thomas M. Fischer (1999), 24 Seiten
Die Anwendung von Balanced Scorecards in
Handelsunternehmen
16
Nr. 33
Dr. Claudia Löhnig (1999), 29 Seiten
Wirtschaftliche Integration im Ostseeraum vor dem Hintergrund
der Osterweiterung der Europäischen Union: eine
Potentialanalyse
Nr. 34
dieses Arbeitspapier ist nicht mehr verfügbar
Nr. 35
Prof. Dr. Bernhard Schwetzler (2000), 31 Seiten
Der Einfluss von Wachstum, Risiko und Risikoauflösung auf den
Unternehmenswert
Nr. 36
Dr. Thomas Hutzschenreuter / Albrecht Enders (2000),
27 Seiten
Möglichkeiten zur Gestaltung Internet-basierter Studienangebote
im Markt für Managementbildung
Nr. 37
Dr. Peter Kesting (2000), 26 Seiten
Lehren aus dem deutschen Konvergenzprozess – Eine Kritik des
„Eisernen Gesetzes der Konvergenz“ und seines theoretischen
Fundaments
Nr. 38
Prof. Dr. Manfred Kirchgeorg / Dr. Peggy Kreller (2000),
31 Seiten
Etablierung von Marken im Regionenmarketing – eine
vergleichende Analyse der Regionennamen "Mitteldeutschland"
und "Ruhrgebiet" auf der Grundlage einer repräsentativen Studie
Nr. 39
Dr. Peter Kesting (2001), 23 Seiten
Was sind Handlungsmöglichkeiten? – Fundierung eines
ökonomischen Grundbegriffs
Nr. 40
Dr. Peter Kesting (2001), 29 Seiten
Entscheidung und Handlung
Nr. 41
Prof. Dr. Hagen Lindstädt (2001), 27 Seiten
Decisions of the Board
Nr. 42
Prof. Dr. Hagen Lindstädt (2001), 28 Seiten
Die Versteigerung der deutschen UMTS-Lizenzen – Eine
ökonomische Analyse des Bietverhaltens
Nr. 43
PD Dr. Thomas Hutzschenreuter / Dr. Torsten Wulf (2001),
23 Seiten
Ansatzpunkte einer situativen Theorie der
Unternehmensentwicklung
Nr. 44
Prof. Dr. Hagen Lindstädt (2001), 14 Seiten
On the Shape of Information Processing Functions
17
Nr. 45
PD Dr. Thomas Hutzschenreuter (2001), 18 Seiten
Managementkapazitäten und Unternehmensentwicklung
Nr. 46
Prof. Dr. Wilhelm Althammer / Christian Rafflenbeul (2001),
42 Seiten
Kommunale Beschäftigungspolitik: das Beispiel des Leipziger
Betriebs für Beschäftigungsförderung
Nr. 47
Prof. Dr. Thomas M. Fischer / Dr. Petra Schmöller (2001),
32 Seiten
Kunden-Controlling – Management Summary einer empirischen
Untersuchung in der Elektroindustrie
Nr. 48
Prof. Dr. Manfred Kirchgeorg / Eva Grobe / Alexander Lorbeer
(2003), (noch nicht erschienen) 56 Seiten
Einstellung von Talenten gegenüber Arbeitgebern und regionalen
Standorten : eine Analyse auf der Grundlage einer Befragung von
Talenten aus der Region Mitteldeutschland
Nr. 49
Prof. Dr. Manfred Kirchgeorg / Alexander Lorbeer (2002),
60 Seiten
Anforderungen von High Potentials an Unternehmen – eine
Analyse
auf der Grundlage einer bundesweiten Befragung von High
Potentials und Personalentscheidern
Nr. 50
Eva Grobe (2003) 78, XXVI Seiten
Corporate attractiveness: eine Analyse der Wahrnehmung von
Unternehmensmarken aus der Sicht von High Potentials
Nr. 51
Prof. Dr. Thomas M. Fischer / Dr. Petra Schmöller /
Dipl.-Kfm. Uwe Vielmeyer (2002) 35 Seiten
Customer Options – Möglichkeiten und Grenzen der Bewertung
von kundenbezogenen Erfolgspotenzialen mit Realoptionen
Nr. 52
Prof. Dr. Thomas M. Fischer / Dipl.-Kfm. Uwe Vielmeyer
(2002), 29 Seiten
Vom Shareholder Value zum Stakeholder Value? – Möglichkeiten
und Grenzen der Messung von stakeholderbezogenen
Wertbeiträgen
Nr. 53
Carsten Reimund (2002), 34 Seiten
Internal Capital Markets, Bank Borrowing and Investment:
Evidence from German Corporate Groups
Nr. 54
Dr. Peter Kesting (2002), 21 Seiten
Ansätze zur Erklärung des Prozesses der Formulierung von
Entscheidungsprozessen
18
Nr. 55
Prof. Dr. Wilhelm Althammer / Susanne Dröge (2002), 27
Seiten
International Trade and the Environment: The Real Conflicts. Pdf-Dokument
Nr. 56
Prof. Dr. Bernhard Schwetzler / Maik Piehler (2002), 35 Seiten
Unternehmensbewertung bei Wachstum, Risiko und Besteuerung
– Anmerkungen zum „Steuerparadoxon“
Nr. 57
Prof. Dr. Hagen Lindstädt (2002), 12, 5 Seiten
Das modifizierte Hurwicz-Kriterium für untere und obere
Wahrscheinlichkeiten - ein Spezialfall des ChoquetErwartungsnutzens
Nr. 58
Karsten Winkler (2003), 25 Seiten
Getting Started with DIAsDEM Workbench 2.0: A Case-Based
Tutorial
Nr. 59
Karsten Winkler (2003), 31 Seiten
Wettbewerbsinformationssysteme: Begriff, Anforderungen,
Herausforderungen
Nr. 60
Prof. Dr. Bernhard Schwetzler / Carsten Reimund (2003),
31 Seiten
Conglomerate Discount and Cash Distortion: New Evidence from
Germany
Nr. 61
Prof. Pierfrancesco La Mura (2003), [10] Seiten
Correlated Equilibria of Classical Strategic Games with Quantum
Signals
Nr. 62
Prof. Dr. Manfred Kirchgeorg (2003), 26 Seiten
Markenpolitik für Natur- und Umweltschutzorganisationen
Nr. 63
Stefan Wriggers (2004), 32, XXV Seiten
Kritische Würdigung der Means-End-Theorie im Rahmen einer
Anwendung auf M-Commerce-Dienste
Nr. 64
Prof. Pierfrancesco La Mura / Matthias Herfert (2004),
18 Seiten
Estimation of Consumer Preferences via Ordinal DecisionTheoretic Entropy
Nr. 65
Prof. Dr. Bernhard Schwetzler (2004), 31 Seiten
Mittelverwendungsannahme, Bewertungsmodell und
Unternehmens- wertung bei Rückstellungen
19
Nr. 66
Prof. Dr. Manfred Kirchgeorg / Lars Fiedler (2004), 47 Seiten
Clustermonitoring als Kontroll- und Steuerungsinstrument für
Clusterentwicklungsprozesse - empirische Analysen von
Industrieclustern in Ostdeutschland
Nr. 67
Prof. Dr. Manfred Kirchgeorg / Christiane Springer (2005),
39 , XX Seiten
UNIPLAN LiveTrends 2004/2005 : Effizienz und Effektivität in der
Live Communication ; Eine Analyse auf Grundlage einer
branchenüber-greifenden Befragung von Marketingentscheidern in
Deutschland
Nr. 68
Prof. Pierfrancesco La Mura (2005), 11 Seiten
Decision Theory in the Presence of Uncertainty and Risk
Nr. 69
Prof. Dr. Andreas Suchanek (2005), 25 Seiten
Is Profit Maximization the Social Responsibility of Business?
Milton Friedman and Business Ethics
Nr. 70
Prof. Dr. Ralf Reichwald / Prof. Dr. Kathrin Möslein (2005),
48 Seiten
Führung und Führungssysteme
Nr. 71
Prof. Dr. Manfred Kirchgeorg / Christiane Springer (2005)
360º Kommunikation im Kundenbeziehungszyklus : Eine Analyse
auf Grundlage einer branchenübergreifenden Befragung von
Marketing-Entscheidern in Deutschland
(noch nicht erschienen)
Nr. 72
Prof. Pierfrancesco La Mura / Guido Olschewski (2006),
8 Seiten
Non-Dictatorial Social Choice through Delegation