Running Head: NETWORKS AND THE GAME OF CHICKEN Network Structure and Strategy Evolution in the Game of Chicken Frank Tutzauer Pauline W. Hoffmann Margaret K. Chojnacki State University of New York at Buffalo International Sunbelt Social Network Conference XXII International Network for Social Analysis New Orleans, LA February 15, 2002 Network Structure 2 Abstract Cellular automata have long been used to study self-organization, system evolution, and questions of dynamics and transformation. Beginning in the 1980’s, researchers used cellular automata to study cooperation in the iterated Prisoner’s Dilemma (PD). For these researchers, a cellular automaton is a lattice-like spatial grid consisting of interlinked cells. Each cell is occupied by an organism that adopts a certain PD strategy, and each organism plays the iterated PD with organisms in neighboring cells. After play, each organism decides to either retain its strategy or adopt that of one of its neighbors, depending on the relative success of the strategies. In this way, researchers show how cooperative strategies evolve based on the initial distribution of strategies and the make up of the population. In this paper, we use a network approach to answer similar questions about strategy evolution in the game of Chicken, a matrix game that models phenomenon as diverse as species competition, the California energy crisis, the NATO/Milosevic conflict, and the current war on terrorism. We make the natural identification between a network and a cellular automaton by equating cells of the automaton to nodes of a network, and considering two nodes to be adjacent if they are neighboring cells in the automaton. We label the nodes of the network with the particular strategies played, have each strategy play those strategies to which it is adjacent (in the network sense), and then change the labels on the basis of local strategy performance. Once we think of the strategies as evolving in a network, instead of in the classic spatial automaton, we can ask questions of structure. In this paper, we suggest various network structures, and for each network structure we conduct computer simulations to determine the evolution of strategies in the network. Network Structure 3 Network Structure and Strategy Evolution in the Game of Chicken Introduction Game theory can be seen in use in mathematics, biology, economics, management, communication, and political science. Scientists and researchers in various social and natural science disciplines, from John von Neumann in mathematics, to Robert Axelrod in political science, to Frank Tutzauer in communication, have studied both Chicken and Prisoner’s Dilemma (PD), two distinct and commonly studied games. They have also examined strategies and their evolution in conflict situations (Axelrod, 1997, 1984, 1980a, 1980b; Feeley, et.al, 1997; von Neumann, 1966). Modern game theory, commonly attributed to John von Neumann (1928; 1937) has the following features (Luce & Raiffa, 1957, p. 2-3): The possible outcomes of a given situation are well specified and the player(s) has a consistent pattern of preferences among the outcomes. The variables controlling the outcomes are also well defined. Each individual player strives to maximize his/her utility. Each player knows the preferences of the other player(s). Prisoners Dilemma The PD fits this game theory with its own defined set of rules. The PD is a matrix game used to show how cooperative or competitive choices influence the result of a decision making process (Axelrod, 1984). Most notably, it contains a dilemma. The distinguishing feature of the Prisoner’s Dilemma is that in the short run, neither side can benefit itself with a selfish choice enough to make up for the harm done to it from a Network Structure 4 selfish choice by the other. Thus, if both cooperate, both do fairly well. But if one defects while the other cooperates, the defecting side gets its highest payoff, and the cooperating side is the sucker and gets its lowest payoff. This gives both sides an incentive to defect. The catch is that if both do defect, both do poorly. (Axelrod, 1980a, p.4) By encompassing the motivation of both sides to be selfish, while maintaining the circumstance of a higher payoff with mutual cooperation over mutual defection (see Table 1), “the Prisoner’s Dilemma embodies the tension between individual rationality … and group rationality…” (p.4). Initial PD games, as in Axelrod’s (1980) computer tournaments, began with 2x2 games. These allowed for only two players, each of who can choose between two actions, typically called cooperation and defection. While this may be helpful to understand the PD itself, “rare is the conflict in which disputants have only two strategies available to them” (Tutzauer, 1989, p.1). From here, we progressed to the 5x5 matrix, which expands the choices from merely cooperate, C, and defect, D, to levels of C and D on a scale of 1 to 5 with 1 being total cooperation and 5 being total defection (To, 1988). Further expansion of the PD takes us to the infinite-choice, continuous-time PD, in which players have an infinite number of choices between 0 (total defection) and 1 (total cooperation) (Feeley, Tutzauer, Rosenfeld, & Young, 1997). This mimics everyday conflicts, which “evolve in continuous time” rather than taking place at well defined moves (Tutzauer, 1994, p.6). Chicken Chicken game first gained recognition in the 1950’s as a game in which teenagers would drive their cars quickly at one another. The first to swerve was considered the chicken. The payoffs in Network Structure 5 Table 1: Payoff Matrix of the Prisoner’s Dilemma Cooperate Cooperate Defect 3 3 Defect 5 0 0 5 1 1 Note. In each cell, the 1st number (row 2 and 4) is the payoff to the row player and the 2nd number (row 1 and 3) is the payoff to the column player. Network Structure 6 this case can be considered severe. If neither party swerves, both parties could die (or be critically injured). If one party swerves, that party seems to ‘lose face’ or face ridicule by friends and onlookers. In this case, it seems to be a game of pride and stupidity (Luce & Raiffa, 1957). Chicken can also be examined from the point of view of two players who each have a certain amount of money or power to ‘invest’, with payoffs following the Chicken payoff matrix (Bornstein, 1997; see Table 2). The investment that each player can choose to make is 2 (points, dollars, or other units). If both players don’t invest, both maintain what would have been their initial investment (2 units). If one player invests while the other does not, the investing player receives the investment of 2 units back plus a bonus of 3 units, while the non-investing player keeps his/her initial 2 units. If both invest, both lose their 2 units and gain nothing in return. This payoff matrix differs markedly from that of the PD. While in the PD, an evolution of cooperation is the better choice for the collective (not the individual player), the best collective payoff in Chicken seems to be a conciliation with the other player to invest every other turn, thus receiving seven rather than four (by both never investing) or zero (by both always investing) units in two moves. Game Theory Usage According to Fink (1998), game theory can be used to: explore theoretical problems that arise from development of game theory. analyze actual strategic interactions in order to predict or explain the actions of actors involved: How can a leader get a follower to do what he wants him to do or how effective are international sanctions? Network Structure Table 2: Payoff Matrix in the Chicken Game Do Not Invest (Swerve) Do Not Invest (Swerve) Invest (Don’t Swerve) Invest (Don’t Swerve) 2 2 5 2 2 5 0 0 Note. In each cell, the 1st number (row 2 and 4) is the payoff to the row player and the 2nd number (row 1 and 3) is the payoff to the column player. 7 Network Structure Examine specific cases (such as the Cuban Missile Crisis or other military conflicts.) Analyze logical consistency of certain arguments. 8 Recent articles referencing current events have referred to game theory more and more to help predict and explain the circumstances. The 2001 California energy crisis involved a game of chicken between the California government and the energy producers (“California’s Giant,” 2001). The government demanded cooperation from the energy producers in terms of a windfall-profits tax, price caps, price cuts and payment on the $5.5 billion tab the government claimed the energy producers owed. The energy producers wanted to avoid price caps and reductions and threatened to stop building power plants as a result. Each “player” has a certain “unit” to invest and a certain “unit” at stake. Each is driving head on at the other. If neither swerves, the constituents may face blackouts and higher prices making the government look bad while the energy producers will be blamed and also look bad to customers, lose money for employees and boards of directors and not have further investment in additional power plants (0/0 payoff matrix). If the California government swerves while the energy producers do not, the California government will look weak (will not save face – payoff of 2 units) in the eyes of its constituents while the energy producers will look good in the eyes its employees and boards of directors (payoff of 5 units). If the energy producers swerve, they will have saved face with their customers by lowering prices and preventing blackouts while showing cowardice to the employees and boards of directors (payoff of 2 units) while the government will be the big winners having refused to give in (payoff of 5 units). If both swerve (each with a payoff of 2) they will both look good to customers and constituents but one will not have an advantage over the other and neither will look as good if one didn’t swerve while the other did. Network Structure 9 Appendix 1 highlights additional examples of chicken played in various arenas from economics to politics to communication. Based on the assumptions of game theory mentioned earlier, why is it difficult to predict behavior? According to Luce and Raiffa (1957), in bargaining, negotiating, mediating, and arbitrating, there is a conflict or struggle between at least two interdependent parties who perceive: incompatible goals scarce rewards interference from the other party in achieving the goals Bargaining, negotiating, mediating, and arbitrating involve a series of decisions based on strategies. A ‘player’ must choose a strategy that covers all possible special circumstances that may arise. It is difficult to specify strategy sets available due to possible modification of strategies during play. There needs to be a specification of time, and also the possibility for coalition. Neither side has complete control over the bargaining situation, and the outcomes are determined by a series of battles, of which the timing is important (Luce & Raiffa, 1957). Conflict can be resolved by conciliation and/or collusion (Luce & Raiffa, 1957). To date, no computer simulations have been able to take the above situations into consideration. Most deal with one programmed strategy that does not change. That strategy then plays another strategy, which is programmed to be just as rigid. To be more representative of real life negotiation circumstances, a program must encompass the ability for its strategies to change, adapt, or evolve, depending on the situation. Examining game theory in the context of a cellular automata matrix can do this. Network Structure 10 Cellular Automata A cellular automaton was first proposed by von Neumann (1966) (considered to be the father of modern game theory) in an effort to examine “the important similarities between computers and natural organisms” (p. 18). His “theory of automata” was developed as a result of his knowledge of artificial and natural systems, in order to examine (von Neumann, 1966, p.21): A coherent body of concepts and principles concerning the structure and organization of both natural and artificial systems. The role of language and information in such systems. The programming and control of such systems. By seeing economic systems as natural systems, and games as artificial systems, von Neumann also developed a connection between his “theory of automata” and “game theory”,. “The theory of games contains the mathematics common to both economic systems and games just as automata theory contains mathematics common both to natural and artificial automata (1966, p.19 or 92?): Logical universality – when is a class of automata able to perform all logical operations that are performable with finite means? Constructability – can the automata be constructed by another automaton? Construction-universality – Can one automaton construct every other automaton? Self-reproduction – can one automaton construct an identical automaton? Evolution – can the construction of automata by automata progress from simpler types to increasingly complicated types (or from less efficient to more efficient)? Network Structure 11 In keeping with game theory, he noted that conflicts between organisms lead to consequences (natural selection), a mechanism of evolution. So, conflict brings about evolution (von Neumann, 1966). To simplify cellular automata and “theory of automata”, Ian Stewart uses “theory of automata” in reference to ecology and population dynamics. “Cellular automata are composed of a large grid of squares, called cells, and each square is governed by its own ‘laws of nature’” (Stewart, 1998, p.36). Axelrod developed a theory that is quite similar called the Landscape Theory of Aggregation (Axelrod, 1997). This theory organizes elements by putting highly compatible elements together, and less compatible elements elsewhere. He has used his theory to predict social circumstances such as military and corporate alliances, social networks, and organizational structures (Axelrod, 1997). Additionally, Axelrod developed a model to discover complex and simple strategies adapted to a complex environment. The genetic algorithm (Axelrod, 1997, p. 15) can be used in the PD environment of his computer tournaments or the chicken games in the present study’s cellular automata network structures. The genetic algorithm involves the following steps (Axelrod, 1997, p. 15): The specification of an environment in which the evolutionary process can operate. The specification of the genetics, including the way information is translated into a strategy. The design of the experiment to study the effects of alternative realities. The running of the experiment for a specified number of generations on a computer. Network Structure 12 Cellular automata can also “tell us a lot about self-organization. …Starting from a primordial soup of initial conditions, these rules show extremely simple ways to generate complex structures. From a complete mess, one can watch organization emerge” (Lipkin, 1994, p.109). Current Study In this paper, we use a network approach to answer similar questions about strategy evolution in the game of Chicken, a matrix game that models phenomenon as diverse as species competition, the California energy crisis, the NATO/Milosevic conflict, and the current war on terrorism. We make the natural identification between a network and a cellular automaton by equating cells of the automaton to nodes of a network, and considering two nodes to be adjacent if they are neighboring cells in the automaton. We label the nodes of the network with the particular strategies played, have each strategy play those strategies to which it is adjacent (in the network sense), and then change the labels on the basis of local strategy performance. Method Seven general strategies were studied in a cellular automata-like network, in order to model strategy evolution in varying network structures. Next, computer simulations were preformed over time with competing strategies ‘evolving’ to those ‘cells’ around them that were most successful. The cellular automata program written by Tutzauer utilizes the computer to set up these cells. Each cell contains one strategy and each cell ‘plays’ chicken against all cells adjacent to it, based on the payoff matrix in Table 1. After each cell plays chicken with each of Network Structure Figure 1: Example of a Cellular Automaton 1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4 Note. Strategy 5 is playing against all strategies surrounding it (its local neighborhood). After one generation of play (a generation is the time it takes for each cell in the matrix to play each surrounding cell throughout the matrix), the cell containing strategy 5 will either remain with strategy 5, or, depending on the payoff results of its neighboring cells, adopt another strategy. This will depend on which of its neighbors, including itself, had the highest payoff. 13 Network Structure 14 its neighbors (signifying one generation), each strategy then ‘evolves’ to the strategy that earned the most points in its Chicken game. A miniature version of the cellular automata with strategies numbered 1 through 5 is represented in Figure 1. This program closely resembles the cellular automata as discussed by von Neumann (1966) and the genetic algorithm as outlined by Axelrod (1997). Tutzauer’s program is able to determine how strategies will evolve and, if a pattern or periodicity emerges. As well, this program may act as a precursor for further research to predict outcomes involving military and organization conflict and other areas of communication conflict. The cellular automata program developed by Tutzauer (19?) is written in BASIC computer language. The following parameters can be set and adjusted: Any number of strategies can be run in the program and any combination of strategies can be run. For example, if 25 strategies are programmed, all 25 can be run at once or selected strategies can be run against each other. (In the current study, seven strategies were run). Any combination of starting strategies can be selected (In the current study, a random setup was used). Any percentage of starting strategies can be set (In the current study, all strategies being played are present initially in equal proportions). The nodes/cells in the network can be predetermined, as can the structure of the automata (In the current study, five different structures were used). Any number of generations can be run For this experiment, the simulations were run using seven strategies: Strategy 1 – Invest every turn Strategy 2 – Invest every other turn Network Structure Figure 2: Representation of a Spatial Grid 15 Network Structure Strategy 3 – Invest every third turn Strategy 4 – Invest every fourth turn Strategy 5 – Invest every fifth turn Strategy 6 – Invest every sixth turn Strategy 7 – Never Invest 16 The cellular automata matrix structure (shown in Figure 1) can easily be translated into various network structures. The simplest, the Spatial Grid (see Figure 2), shows the interconnectedness of the neighbors in the matrix. Note that the inner nodes of the grid play eight neighbors while the edges play five and the four corners play only three. The second structure examined is a Regularized Spatial Grid (see Figure 3). This structure closely resembles the Spatial Grid, however, the edges and corners have been “regularized” to play eight other neighbors. In this structure, all nodes are connected to eight other nodes. In both the Spatial and Regularized Grids, the network consisted of a 200 x 200 matrix. The Bipartite Network structure represented in Figure 4 corresponds to a “segregated” network pattern of 100 nodes for each “side.” A side can represent gender (male/female chicken encounters), religion (protestant/catholic chicken interactions), or bipartisan politics (democrats/republicans), to name a few. Each player in this network plays chicken against three members of the opposite partite, and none in its own partite. Figure 5 represents the Star Network. It is characterized by a radial or wheel-like network in which the central figure in the star plays Chicken against eight neighbors while the outside nodes play only one and the inner nodes, two. The Star is composed of # of nodes and branches. Network Structure Figure 3: Representation of the Regularized Spatial Grid Structure 17 Network Structure Figure 4: Representation of the Bipartite Network Structure 18 Network Structure Figure 5: Representation of the Star Network Structure 19 Network Structure 20 The 400-node Chain Network is the final structure and is represented in Figure 6. The ends of the chain play only one other node, while the inner nodes play two others. This structure is similar to the Star Network, but without the central node figure. Each simulation was run in five different episodes (differing starting values/initial conditions) with each of the five network structures. The simulation ran until the program detected a periodic pattern. After each generation, the number and type of strategies still existing was recorded for later examination. Upon completion of a run, the number of steps required to find a period, the period itself (how long the repeating pattern/string is), and the strategies left after periodicity is reached, were recorded. Results Table 3 represents a summary of the results. The Spatial Grid reached a period after 117, 84, 180, 115 and 142 steps, with periods of 12, 24, 66, 2 and 4. Strategy 1 (Always Invest) survived in all cases with strategies 3, 4, 5, 6 and 7 surviving in different runs. A graphical example of this periodicity for run number 1, which achieved a 12-cycle period, can be seen in Figure 7. All strategies were replaced fairly quickly by strategies 1 and 7, which didn’t reach a period until generation 117. At this point, it can be seen that the population size fluctuates from larger to smaller depending on the generation and population of the other strategy. The Regularized Spatial Grid reached periods of 2 and 12 after 97, 130, 169, 180 and 107 generations. The strategies remaining always included Strategy 1 (always invest), with Strategy 7 in the first run and Strategy 5 in all subsequent runs. Network Structure Figure 6: Representation of the Chain Network 21 Network Structure 22 The Bipartite Network structure took quite a number of generations (3790, 1467, 2204, 3062, and 1435), and reached a periodicity of 6 or 2. Again, Strategy 1 dominated, with Strategy 7 also present in run 2, and Strategy 5 present in all other runs. The 6-cycle period of run 5 can be seen in Figure 8. Only strategy 5 and 1 are present. All other strategies died shortly after the start of the simulation. The Star Network reached a 2-cycle each time in a relatively few generations (64, 34, 58, 85, and 56). Most strategies survived in some number. Strategies 1 through 6 survived in most cases, with Strategies 1 through 5 surviving in run 2. Figure 9 shows the 2-cycle with all strategies or just the 2 bottom dwellers?) The Chain Network reached a 2-cycle each time in a varied number of generations (130, 53, 132, 173, and 70). Again, most strategies were present, from Strategies 1 through 6 in runs 1, 4 and 5, and Strategies 1 through 5 in runs 2 and 3. Conclusions We found several patterns across all the network structures studied, as well as patterns that were unique to each structure. Across All Network Structures Across all the network structures, all systems seemed to converge in “short” times with “small” periods. Strategy 1 (Always Invest) does extremely well and is represented in all runs for all network structures. In each case, the network system evolves to an even periodicity. No fixed points were present in this simulation. Network Structure 23 Table 3: Results Number Steps (how many steps to find a period) Period (how long is the repeating string) Strategies Left (what strategies survived after simulation complete) Spatial Grid 1 2 3 4 5 117 84 180 115 142 12 24 66 2 4 1,7 1,3,5 1,5 1,5,6 1,5,4 1 2 3 4 5 97 130 169 180 107 2 12 2 2 12 1,7 1,5 1,5 1,5 1,5 1 2 3 4 5 3790 1467 2204 3062 1435 6 6 2 6 6 1,5 1,7 1,5 1,5 1,5 1 2 3 4 5 64 34 58 85 56 2 2 2 2 2 1-6 1-5 1-6 1-6 1-6 1 2 3 4 5 130 53 132 173 70 2 2 2 2 2 1-6 1-5 1-5 1-6 1-6 Regularized Spatial Grid Bipartite Network Star Network Chain Network Network Structure Figure 7: Graph of 12-Cycle in Spatial Grid 24 Network Structure Figure 8: Graph of 6-Cycle in Bipartite Network 25 Network Structure Figure 9: Graph of 2-Cycle in Star 26 Network Structure 27 Between Networks The Star and Chain Network structures evolved small, even periods of a two-cycle. The Bipartite and Regularized Spatial Grids evolved short to medium even periods (between 2 and 12 cycles). The Spatial Grids evolved even periods ranging from short to very long (between 2 and 66 cycles). The Star Network structures evolved to periodicity in a short number of generations (between 34 and 85 generations). Chains, Regularized and Spatial Grids reached a periodicity in a medium number of generations (from 53 to 180). It took Bipartite Networks a large number of generations (from 1435 to 3790) to evolve. Star and Chain Networks managed to keep all strategies alive except Strategy 7 (never invest). Strategy 1 (always invest) dominates while the others barely hang on. The Spatial Grid allowed two to three strategies to challenge Strategy 1. With Regularized Spatial Grids and Bipartite Networks, a strong competitor (usually Strategy 5) emerges to challenge Strategy 1. Discussion This study was a preliminary foray into chicken game and network structure simulations. Further research will include examining different strategies, modeled after games of Chicken represented in Appendix 1, to determine if, based on different network structures, certain strategies bode well in bargaining/negotiating situations. Limitations This was a preliminary study. The network structures and strategies that were used were not theory driven. Hence, they were primitive in their scope. However, this study was used Network Structure 28 primarily to understand the basic operations of the cellular automata as a network structure, and it served that purpose. Thus, the results present many avenues for future study. Future Research A future simulation could involve non-random starting patterns with the basic strategies used in this paper and further strategies developed. These simulations will be run using structures as in this paper, except the strategy pattern at the onset will vary. The configurations of strategies will be determined in a couple of ways. First, a simulation run will begin with clumped strategies evenly distributed and represented. Patterns can also be based on ending patterns of this simulation in terms of strategy configurations present. For example, if Strategy 1 were dominant, then it would be a dominant cluster in this simulation with a proportional representation as its ending pattern. With this in mind, some strategies may not be represented at all since, presumably, strategies will have become extinct from the original simulation. Also, any combination of ‘random’ cluster configurations can be run. The second avenue to pursue in simulations is that of adding a threat potential. This process would be run again, but this time a weight would be added to the strategies that are successful. It is not often that bargaining and negotiating takes place on an even playing field with a clean slate. The slate could be kept clean (that is all strategies begin having zero points) or different configurations of threat potential could be used. Once one strategy reaches a certain point value or obtains a certain percentage of a lead (say 10%) then the payoff matrix changes. A potential change could be as follows (assuming the row player is the player in the lead giving him/her the greater threat potential): Network Structure 29 column player Invest Invest Don’t Invest 2.5/1.5 2.5/4.5 row player Don’t Invest 5.5/1.5 .5/-.5 This is just an example. The actual payoff matrix change could be based on percentage of the lead, or population size of the strategies after each generation. The simulation will be run as above with random placement and then non-random clusters placed. Borrowing from the biological MacArthur Wilson Theory of Island Biogeography, “barriers” can be inserted into the network structures to determine if a different evolution will occur if an obstacle is present. It would also be valuable to examine whether of not the size of the network structure would make a difference in terms of strategy evolution. Varying the size of the network matrix, for example, from 200 x 200 to 100 x 100 or 400 x 400, would likely cause a change in results. It would be ideal to try to maximize the size the matrix in order to make the cellular automata environment, which by definition is finite, as illustrative of reality as possible. Finally, examining the possibility of an evolving structure within the automaton itself would be fruitful. By expanding the interpretations of the traditional cellular automata, and manipulating it in as many ways as theoretically possible, future work only stands to expand the knowledge provided through simulation. Network Structure 30 Appendix 1 Examples of Chicken Game: California Energy Crisis (“California’s Giant,” 2001) The 2001 California energy crisis involved a game of chicken between the California government and the energy producers. The government demanded cooperation from the energy producers in terms of a windfall-profits tax, price caps, price cuts and payment on the $5.5 billion tab the government claimed the energy producers owed. The energy producers wanted to avoid price caps and reductions and threatened to stop building power plants as a result. Each “player” has a certain “unit” to invest and a certain “unit” at stake. Each is driving head on at the other. If neither swerves, the constituents may face blackouts and higher prices making the government look bad while the energy producers will be blamed and also look bad to customers, lose money for employees and boards of directors and not have further investment in additional power plants (0/0 payoff matrix). If the California government swerves while the energy producers do not, the California government will look weak (will not save face – payoff of 2 units) in the eyes of its constituents while the energy producers will look good in the eyes its employees and boards of directors (payoff of 5 units). If the energy producers swerve, they will have saved face with their customers by lowering prices and preventing blackouts while showing cowardice to the employees and boards of directors (payoff of 2 units) while the government will be the big winners having refused to give in (payoff of 5 units). If both swerve (each with a payoff of 2) they will both look good to customers and constituents but one will not have an advantage over the other and neither will look as good if one didn’t swerve while the other did. NATO/Milosevic (Hirsh, 1999) In the conflict between Milosevic and NATO, neither side wanted to concede/swerve (both sides were driving very quickly and dangerously toward one another). This may be an example closest to the original intend of the game of Chicken. In addition to the obvious loss of life by both sides and other atrocities, to concede defeat would effectively require that one side lose face in world politics. If neither side swerved and continued toward one another, devastation of life and land would result and neither player would fare well in the eyes of the world (0 units). If Milosevic surrenders, he will certainly lose face with his followers and perhaps look the coward in the world arena (2 units) while the NATO forces would emerge victorious having defeated such an enemy (5 units). If NATO swerves, they will look the coward and will lose much power in the world arena (2 units) while Milosevic will have emerged victorious and look glorious to his followers (5 units). Game of Chicken in Detroit (Zuckerman, 1998) In Detroit, Knight-Ridder and Gannett wanted to join the forces of their two papers into one to save money for both corporations. This situation would have led to a monopoly and the risk of losing an additional editorial voice (leaving Detroit a one paper city). The Attorney General stepped in to preserve the editorial voice of the two papers by proposing a joint operating Network Structure 31 agreement and prevent a monopoly situation. If the Attorney General and the media giants didn’t reach an agreement, both would lose by remaining at a standstill – the media wouldn’t consolidate and thus lose money and the ability to consolidate papers and the Attorney General would not have reached any agreement (0 units). If Knight-Ridder and Gannett concede, they lose the opportunity to consolidate but may operate under a joint operating agreement allowing for some profit (2 units) while the Attorney General would have prevented a monopoly and preserved the editorial voices of the city of Detroit (5 units). If the Attorney General swerves while the media does not, he loses editorial voice (2 units) while Knight-Ridder and Gannett consolidate and save money (5 points). Network Structure 32 References Axelrod, R. (1980a). Effective choice in the Prisoner’s Dilemma. Journal of Conflict Resolution, 24, 3-25. Axelrod, R. (1980b). More Effective choice in the Prisoner’s Dilemma. Journal of Conflict Resolution, 24, 379-403. Axelrod, R. (1984). The Evolution of Cooperation. New York, NY: Basic Books, Inc., Publishers. Axelrod, R. (1997). The Complexity of Cooperation. Princeton, NJ: Princeton University Press Bornstein, G., Budescu, D., & Shmuel, Z. (1997). 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