The Microfinance Game
Kathleen Rodenburg
Abstract
Game theory is applied to intuit how group borrowers play the microfinance
game with the microfinance institution to provide some theoretical evidence as
to why microfinance institutions may have shifted their focus away from group
solidarity lending practices. The leveraging of the social connections within a
collective society by the Microfinance institution can be the same tool used by
the borrowing group to collude against the institution. Results show borrowers
can maximize their expected payoffs by playing a risky investment strategy at
some point during the game. And when the amount of times playing the risky
investment strategy increases, the probability of default on loan repayments
increases. Furthermore, if risky strategies are employed early on and the game
does not end, the expected payoff from choosing the risky strategy in the future
also increases relative to playing it safe. As repayment rates decline, the
microfinance institution perforce must play their “no group loan” strategy
choice.
Introduction
Muhammad Yunus (1998), founder of the Grameen Bank, demonstrated that microfinance is an
effective way to address imperfections in the credit market. In particular, Yunus found a workable
mechanism utilizing joint liability contract features that enables microfinance to make small
uncollateralized loans to groups of poor customers. However, despite repayment rates in excess of 95%
on these unsecured loans, and the successful servicing of over 100 million customers around the world
using these credit practices, microfinance institutions have shifted their lending practices 1 back to
traditional individual lending mechanisms entailing collateral. Armendize de Agion and Murdoch
(2005) suggest that this move is because the current customers have matured and now seek larger loans.
Cull et al. (2007), on the other hand, suggest that mission drift could be the major contributing factor,
i.e., the microfinance institutions have made a conscience shift in the composition of new clients, or
have reoriented their focus from poorer to wealthier clients.
Cull et al. (2007) define the mission of microfinance institutions as “…the reduction in poverty without
dependence on on-going subsidies.” Achieving this goal requires that the institution translate high loan
repayment rates into profit. Although there are no doubt various interpretations of the mission of
microfinance institutions (Yunus (1998), Cull and al(2007), Agion and al(2005), etc..), this definition
provides a good starting point to hypothesize about why microfinance institutions are not engaged in
group loan practices today, despite the aforementioned favourable results. Given that one billion people
globally live in households with per capita income of less than $1 per day(Murdoch, 2007), it seems
unlikely that the microfinance institutions stopped their group lending practices because they achieved
their goals for poverty reduction. What is more likely is that the workable mechanism developed by
1
In 2005, Grameen dropped joint liability completely, and just 1% of Banco Sol’s loan portfolio was under group contracts
in 2005 ( Gine & al, 2005).
1
Yunus was not sustainable in the long-term. Despite the high repayment rates, microfinance institutions
were still highly dependent on subsidization to achieve their poverty reduction goals (cull et al, 2007).
The intention of this paper is to provide some theoretical insight that could help identify the impetus for
microfinance institutions to shift their lending practices from group-based uncollateralized loans to
traditional individual-based loans.
Game theory is applied to intuit how group borrowers play the microfinance game with the microfinance
institution. From a theoretical perspective, the initial positive results from the group lending experience
are puzzling. The group lending mechanism described by Yunus (1998) is vulnerable to moral hazard
problems. In particular, free-riding by individual group members and collusive behavior by the whole
group against the financial institution. Given this, one possible explanation for the aforementioned
positive results is that, initially, the group-based borrowers played the lending game according to the
rules set out by the microfinance institution. As such, they were cautious in their investment strategies to
ensure that the loans were paid back in order to secure loans for the future. However, as play ensued,
groups become savvier on how to play the game to their advantage. Therefore, while group liability is
used to harness the cooperative relationship among the members of the group to the advantage of the
microfinance institution, in time, these same cooperative relationships are used to collude against the
bank. That is, groups begin to make riskier investments to increase their expected payout. This
eventually results in reduced loan repayment rates and a consequent change in the lending practices of
the microfinance institution. Results from the microfinance game applied in this paper suggest just that.
Specifically, once players know the expected payoffs from their investment choices, the optimal
investment strategy for the group is to make at least one risky investment for which the probability of
loan repayment is less than one. And, once the group engages in a risky investment strategy, they are
more likely to continue to choose risky investments for the balance of the game. Hence, as play
continues, the probability of the bank receiving repayment on the loan decreases. Given that to be the
case, the banks are forced to adjust their lending strategy to avoid continuous losses. Namely, as
observed in reality, the microfinance institutions switch back to individual collateralized loan
mechanisms.
The paper is divided into five sections. Section I describes the solidarity group lending mechanism used
by microfinance institutions like the Grameen Bank in Bangladesh. Section II gives insight into the
societal attributes that contribute to the success, and consequent failure, of the microfinance group
lending mechanism described in section I. Section III introduces the microfinance game developed by
this study, and defines the expected payoffs from participation in the game. In particular, the results of
this game show that some risky behavior is optimal and, as may be expected, that the expected payoffs
for risky behavior are greater than prior to engaging in risky behavior.
Section IV provides
comparative statics to illustrate the findings from section III. Finally, section V provides the
conclusions.
2
I. Uncollateralized Group Loan Mechanisms
The following describes the group solidarity lending mechanism as described by Cull et al (2007). In
the initial stage, microfinance institutions set up in a community and announce access to credit with no
collateral required. To qualify for these loans, customers must form small borrowing groups prior to
approaching the micro bank (groups range in size from 3-10 members; e.g., for the Grameen Bank in
Bangladesh groups were comprised of 5 members). The borrowers within the group obtain loans
directly from the bank, and invest the fund separately from the group in keeping with their individual
perception of risk and return. Access to loans continues for all members in the group sequentially, as
long as the previous loan is repaid. The most important element of the solidarity group loan mechanism
is that all group members are jointly liable for repayment of loans made by individual members.
Group liability is used to harness information about each member of the group and their mutual
relationships to the advantage of the microfinance institution. Both moral hazard and poor memberselection problems are reduced. First, it is assumed that individuals who are interested in maximizing
their loan potential will choose other group members who will not free ride on the coat tails of the
group ( i.e., expect other members to repay their loans). Essentially, group members monitor each
other (Banerjee, Besley and Grunnare, 1994) and punish each other with moral sanctions if loans are
defaulted. The underlying key factor for success of the group base lending mechanism is the
assumption that communities with a high degree of social connectedness will threaten peer members
with social penalties to secure repayment of the loans. The next section will investigate how this same
high degree of social connectedness could also result in the group as a whole colluding against the
bank.
II. Collusive Behaviour in Collective Societies
There is not much evaluation and research done in the microfinance sector. Most theoretical models
have focused on the dynamics that occur within the borrower group. Besley and Coate(1995) studied
the repayment game to determine under what conditions will the loan be paid back based on group
interplay. They too assumed that each individual in the group makes their own investment choices and
keeps their winnings, but that all group members share equally the burden of any consequent loss or
default. They also assumed that the group’s ability to punish loan default with social sanctions can
increase repayment rates to the financial institution. Also, as the group has complete information about
incoming members, it is assumed to self-select those members who will not free-ride on the group’s
coattails. The free-rider problem is thus transferred away from the bank by the group. Gine et al (2007)
conducted a series of experimental ‘microfinance games’ over a seven month period in Peru, to
determine how groups play the game against each other, under both cooperative and non-cooperative
assumptions. They found that group liability reduces risk taking and improves the loan repayment rate.
Stiglitz (1990) also suggests moral hazard is reduced due to the high value placed on group
membership within these communities. All of the above studies successful highlight how the joint
liability condition, coupled with the severity of social sanctions in highly connected communities,
eliminates the free-riding concern. However, it is a conjecture of this study that the same conditions
that eliminate free-riding concerns may also intensify the environment for collusive group behavior.
3
The term ‘collectivism’ is used to describe the behaviour inherent in these highly connected
communities. The collectivist social structure is segregated, where individuals socially and
economically interact with members of their own specific religion, ethnic or familial group. Members
of collectivist societies feel involved in the lives of other members of their group. Group membership
is very important for survival. Greif(1994) notes that collectivism is widely practiced in developing
countries, and that cooperation largely at the level of limited groups based on kinship, ethic or special
interest ties, may have potentially large negative effects on economic performance. ‘Cooperation and
trust among these limited groups may facilitate their organization for rent-seeking purposes’ (Greif,
1995). Adam Smith (as quoted in Granovetter, 1985, page 484) states that ‘when people of the same
trade meet even for merriment and diversion, the result is often a conspiracy against the public.’
Knack and Keefer(1997) find in their study that, homogeneous associations in heterogeneous societies
may strengthen trust and cooperative norms within an ethnic group but, at the same time, may weaken
trust and cooperation between groups. In the same way, it is possible that the introduction of the
microfinance institution could be viewed as adversely changing the dynamics of the community.
Specifically, the leveraging of social sanctions by the bank could be viewed as exploitive behavior by
members in the homogeneous community. Although Yunus(1998) describes these group lending
practices as requiring no collateral, the reality is that the micro-banks still rely on a form of collateral
as a basis for extending credit. Rather than collateral in the form of assets, they have successfully
leveraged collateral in the form of social sanctions. Arguably, in a society where social connectedness
is high, social sanctions can be far more damaging to a person than the removal of physical assets. It is
somewhat contradictory that the bank assumes that ‘borrowers’ obtain loans and invest funds
separately, selecting investments based on their individual assessment of risk and return and at the same
time assume that this collective society will impose social sanctions so severe that members of a
group would do anything to pay-back the loan rather than risk community membership.
It seems more reasonable to assume that if the bank can be established as an outsider, the group will
operate under a collective society mentality as one borrowing unit. That is, they would mutually agree
as a group on each sequential investment action choice, and share the windfalls from these investments
equally in the same way that they share the losses. Group members would meet and strategize on how
to play the microfinance loan game in order to maximize the group’s payoff, as opposed to just their
individual payoff.
Hence, the main assumption underpinning the Micro-finance game presented in the following section is
that, a group dictates that ‘a rule of the game’ will be to share the winnings and losses equally amongst
all members. The group therefore, operates as one collective borrower and colludes against the
microfinance institution in order to maximize their expected payoffs. The number of participants in the
group will dictate the maximum number of sequential moves available to the borrower when playing
the game.
4
III. The Sequential N-Rounds, 2-Player Microfinance Game
The microfinance game proposed in this paper focuses on the type of solidarity group loan described in
Section I, where institutions offer contracts based on joint liability to solidarity groups (i.e. the contract
type initially used by the Grameen Bank in Bangladesh, and Banco Sol in Bolvia).
Player 1 is the microfinance institution, whose objective is to reduce poverty by extending loans to the
poorest of the population who have no access to collateral, while decreasing dependence on subsidies.
The Micro-finance institution in each game faces two strategy choices:
Action 1: offer a solidarity group loan
Action 2: do not offer a solidarity group loan
If the loan is offered, the individuals in the group of borrowers are lent a fixed sum of money,
sequentially. Once the borrower group pays back the loan plus some fixed rate of interest, the next
borrower (individual in the group) can receive a loan. If the bank chooses Action 2, no other loan is
extended and the game ends. The bank is assumed to be risk neutral.
Player 2 is represented by a group of borrowers consisting of participants. The objective of player 2
is to arrange their sequential action choices in order to maximize their expected payoffs. In this game,
group members represented by player 2, play the game cooperatively with their own group members
and non-cooperatively with player 1, the bank. We will assume that player 2 is risk neutral2.
The group of members known as player 2, face two action choices for each round of play when a
solidarity group loan is extended:
Action 1: invest in safe a project with certainty of return
Action 2: Invest in a risky project with an uncertain return
Let
be the probability that action 2, results in a successful return, and therefore,
(
) is the probability that action 2 is unsuccessful, where [ ] The size of loan extended from
the lending institution (player 1) for each round of the game is the same, regardless of the investment
action chosen by the borrowing group (player 2) at any stage of the game. The institution cannot see
the action choices of the individual players, only the fact that the loan has been paid back or not. If the
loan is not paid back, the bank needs to determine whether to extend a future loan or not extend a future
loan and end the game. Ideally from the bank’s perspective, the safe investment strategy choice by
player 2 is preferred throughout the entire game, as the bank would then be guaranteed the repayment
of the loan plus some fixed rate of interest.
2
Therefore for simplicity we can assume that expected utility from the investment practices is equal to the expected payoff
functions.
5
It is important to highlight that, while the lender views themselves as interacting with 5 different
investors, the group has consolidated their efforts into one investor. Therefore, any additional loan
extended to a new individual in the group is viewed by the group as a chance to play another round of
the micro-finance game.
This game is, therefore, classified as a sequential game with the maximum number of rounds in the
game equal to (i.e., the number of participants consolidated as player 2). Player 2 plays the game
repeatedly to determine the best investment strategy over time. Groups watch other groups play the
game with the microfinance institution, and converse with other past and future group borrowers, in
order to devise their best strategy. All group members share the earnings of that specific player group,
regardless of when the game ends.
Let the payoff from the safe investment action choice be and let the payoff from the risky investment
choice be , where
(otherwise players would have no incentive to invest in the risky alternative).
Let be the size of loan extended to player 2, by player 1, regardless of whether player 2 intends on
choosing a safe or risky investment action in the next round of play. Set
, where is the
percentage interest rate and, therefore, is the total interest paid on the loan by player 2. It is assumed
that the amount of interest is sufficient to cover the transaction costs associated with extending the
loan. Note that is constant as the size of loan never changes regardless of the action choice of
player 2.
Therefore,
is the net profit from engaging in the safe investment choice, and
is the net profit for a successful risky investment choice by player 2. Given
, we know
that
.
Let be the probability that the risky investment is successful, where
probability that the risky investment will not be successful.
For this game, it is assumed that
[
]. Therefore (
) is the
when making a risky investment.
The extensive form of the micro-finance game is shown as a tree diagram in Figure 1. The micro bank
(player 1) makes the first move and has two action choices, to offer the loan or not. If the loan is
offered, the borrower group(player 2) makes the second move and must decide whether to invest in a
safe investment with certainty of successfully achieving net profit , or invest in a risky investment
with probability of receiving equal to . The expected payoff for player 1 and player 2 is denoted in
brackets; e.g.,
Each player knows their own information at each node in the game. For player 1,
this means the only information available is the past history indicating whether the loan was
successfully paid back or not. For player 2, the information includes knowledge about past safe/risky
investment choices and consequent payoffs, as well as the bank’s payoffs. It is an important aspect of
the game that player 1 does not know at what node player 2 is when the next loan is extended (i.e.
player 1 does not know if player 2 successfully paid back the loan due to a safe or a risky investment
choice in the previous round of play). It is assumed in this game that the bank can creditably commit
not to extend another loan once a failed project is observed. That is, there exists a policy of the bank,
enforced by third party audit, which stipulates that once a loan is in default no further loans can be
6
extended to the group. Therefore, the optimal strategy for the bank if a loan is not paid back is to select
action 2; do not extend a group solidarity loan; and end the game.
Figure 1- Extensive Form of the Sequential 2-Player, 2-Round Microfinance Game
1
Player 2’s information set
{0,0}
2
(1-q)
{-z,z}
q
1
{zi,S}
Player 1’s information set
1
2
{zi,R}
2
(1-q)
(1-q)
{z(i-1),S+z}
q
{2zi,2S}
1
{2zi,S+R}
Microfinance Institution
{z(i-1),R+z}
q
{2zi,R+S}
2
{2zi,2R}
The ‘2 individual’ solidarity group
For each round of play, the expected payoff will change for player 2 based on past action. For
example, the impact on the expected payoff function for player 2 as a consequence of an unsuccessful
risky investment will be different depending on where they are in the sequence of the game. Similarly,
the probability of defaulting on a loan repayment to the microfinance institution will depend on the
investment action choice of player 2 in the previous round of play. Once player 1 extends a group
loan, it is the action choice of player 2 that dictates the payoff functions for both players. Obviously,
given that the loan size is the same regardless of player 2’s action choice, the expected payoffs for
player 1 are maximized when player 2 chooses safe investment actions only. Therefore, we are most
interested in the expected payoffs of player 2 in the sequential microfinance loan game. The outcome
of the game can determined by comparing the expected payoffs from engaging in various sequences of
investment action choices over the course of the game. Specifically, the results of the game can
provide some theoretical insight on whether group-based solidarity loans are sustainable in the long
term.
7
The expected payoff for the risk-neutral borrower (player 2) can be calculated for the -round
sequential microfinance game represented in Figure 1. Let be the number of times the group plays the
[
]. Therefore, the expected payoff for player 2 is,
safe investment strategy, where
Eπ(x,q) = xS +
(
)
(
; where 0≤ x ≤ N and 0<q <1
)
3
(1)
Equation (1) is the sum of the expected payoff for player 2 from playing safe,
expected payoff from playing risky, EπR=
(
)
(
x , plus the
, over the course of the
)
round game. The
expected payoff for the risky strategy can also be written as,
EπR
-
(
(
)
)
(
(2)
)
Proposition 1. For some values of
and , the optimal payoff for player 2 will involve some risky
investments; i.e., the optimal number of safe investment choices
is less than or equal to the total
number of moves available in the game,
.
Proof It suffices to show that, as player 2 chooses safe investments for some values of q, R and S, the
expected payoffs begin to diminish after a number of choices *, that is less than the total number of
rounds available in the game. A necessary condition for * to be an extreme value of the expected
payoff function is for
( *)
. That is, from equation (1),
( )
(
(
)
(
To solve for , let
=
*=
. The solution
(
)
(3)
)
(
)
(
)
, such that Eq.(3) becomes
=
and, hence,
–
* of Eq.(3) is then,
(
)
) =
(
(
)
)
(4)
For * to correspond to a maximum of the expected payoff function, the second order conditions must
be negative, i.e., that Eπ’’(x*)< 0. From equation (3),
3
Note that it is never optimal for player 2 to play the risky action choice first. Although intuitive, the support for this will be
forthcoming.
8
(
)
(
)
(
)
Therefore
(
) has a maximum value at *. The expected payoff to player 2 increases up until *,
while for
*they begin to diminish, indicating that the safe action choice is no longer optimal.
Furthermore, given that ln
for
,
when |
(
(
)
)|
, the optimal value of safe choices * will be less than the available number
of sequential moves in the game; i.e., *
, which indicates that an optimal strategy for player 2
must involve some risky investment action choice.
Proposition 2 . Once player 2 engages in a risky action choice, the expected payoffs from choosing
risky for the balance of the game increase relative to that before the first risky strategy was chosen.
Specifically, the incentives for choosing risky for the balance of the game are greater after a successful
risky investment has been made. Therefore, successful risky investments made early in the game
result in a smaller number of safe investments being made, than if the risky choice was delayed until
near the end of the game(see proposition 1).
Proof When a risky strategy is chosen, an unsuccessful investment ends the microfinance game
because player 2 defaults on the corresponding loan. That is, continuation of the game occurs only
when the risky strategy choice is successful. To maximize the expected payoff for the balance of the
game, player 2 presupposes a probability distribution over the potential remaining rounds of play left in
the game. The incentives of the game change. In particular, the value for q increases since the
occurrence of a successful risky strategy choice results in a shorter game horizon. It can be shown that
as q increases, the expected value of * decreases.
Let
be the probability that a risky investment will be successful. Therefore, at the initial information
node (Figure 1), player 2 presupposes an expected value of
for each round of subsequent play.
Now suppose that player 2 engages in a risky strategy upfront and is successful. Let represent the
number of successful risky strategy choices that occur prior to the final round of the game (
)
Therefore, the initial information node for the next round of play will have an expected value of
(
)
>
.
Now, from equation (4) we know that,
(
(
=
)
(
(
)
)(
)
)
(
(
)
)=0
)
(
Where,
9
Hence,
as
increases (i.e., the optimal value of safe investment choices
* decreases as the
probability that the risky investment will be successful increases).
Let be the number of successful risky strategy choices and, therefore, let (
) represent the total
number of sequential rounds available in the game once the successfu risky strategy has been
employed. Also, let ̅ = (
.
)
Then, from equation (4), the optimal value of ̂ , where ̂ signifies the optimal number of safe
action choices in the game where q value changes as a result of previous successful risky investment
strategies, is,
̂ =(N-Ѳ) +1 +
̅(
(
̅)
̅
),
̂
In the limit as
̂
((
((
)
)
̅(
̅(
(
(
̅)
̅
))
̅)
))
̅
For any amount of risky strategy choices made at the beginning of the game, the optimal value of safe
choices will decrease. As risky strategy play continues, safe strategy choices will continue to decline.
IV. Comparative Statics Using Real Numerical Values
Here, comparative statics are conducted using numerical values for the variables, so as to further clarify
the propositions presented in the previous section.
In scenario 1, to demonstrate the results from proposition 1, let the number of particpants in the group
represented by player 2 be five (i.e., N=5). Also, let the net profits from a safe investment choice
equal $100(S=$100) with certainty, and the net profits from a risky investment choice be
$300(R=$300) with a 50% constant probability of success (i.e.,
), such that qR ($150) >
S($100). Finally, let the number of safe investment choices take on values of zero to five (i.e.,
). From equation (1), we can graph the expected payoffs for player 2 given their selected
value for .
From equation (1), Eπ(x,q) = xS +
(
)
(
and, given
)
, we can calculate the expected payoffs to player 2 based on the number of safe investment
actions chosen.
(
)
(
0 x $100 +
)
(
)
= $290.63
10
Eπ(x,q) = $381.25, $462.50, $525, $550 and $500,
respectively.
And, from equation (4) where * =
* = 5 +1 +
where 0
such that
(
(
(
+
)
(
(
) =6 +
)
) , we can calculate,
(
)= 6+
) ,
and
*= 6 -2 = 4
Figure 2 plots the above results in (
) space. In addition, also plotted are the results when
when
, respectively. For the values of
, player 2 can
optimize their investment strategy by selecting the ‘risky’ action at least once. Interestingly, even when
the best strategy for player 2 is to engage in some risky behaviour as the optimal value of * in
this case is still less than . Therefore, for some values of
, the microfinance game plays out
such that the certainity of the microfinance institution receiving payment on the loan is reduced.
Figure 2- The Expected Payoff Function for Player 2, when Selecting Values of x and when the probability of a Risky
Investment is held constant at 50% (q=.5)
Expected Payoff given 'x' Safe Strategy Choices
Eπ(x,q)
$600.00
qR > S
$500.00
qR = S
$400.00
qR < S
$300.00
$200.00
$100.00
$0.00
0
1
2
x
3
4
x* = 4
5
6
x*< N
Scenario 2 provides an illustration of the results from proposition 2 presented in Section III, which
states that risky investment strategies at the beginning of the game, result in a smaller optimal number
11
of safe investment action choices than if the risky choice is saved for the end of the game. Using the
same values for
as for Scenario 1,we can numerically demonstrate what happens to the
optimal value of x* when we allow the risky strategy choice to occur at the beginning of the game. Let
the number of risky strategy choices
1. Therefore, once the successful risky strategy has been
employed, the number of rounds remaining in the game will be
. By augmenting Equation (1),
we can calculate the impact that this game configuration will have on the expected value of , and
consequently we will be able to determine how this new value of affects the optimal safe investment
strategy choice for player 2.
From equation (1),
Eπ(x, ̅)
+
, ̅ =(
And ̅ =
(
)
)
(̅ ̅(
(
)
)
̅)
,
,
> q =0.5,
For x= 0, Eπ(x, ̅) = 1($300) + 0($100) +
(
(
(
)
)
)
=$300 +423.71 = $723.71
For
is,
1,2,3,4, the Eπ(x, ̅) = $781.84, $809.57, $796.00, $700, respectively, and the optimal value of
̂ =(N-Ѳ) +1 +
̅(
(
̅)
̅
) = (5-1)+1+
where
̂
̂
(
(
)
)
5+
(-0.26595)
and
(
)
and,
< x* = 4
Therefore, engaging in a risky investment action choice at the beginning of the game, if successful,
changes the probability of success from risky investments for the balance of the game. The optimal
value for decreases with the addition of this new assumption from proposition 2. Figure 3 shows the
impact of this new game configuration relative to the results found in scenario 1 concerning
proposition 1, where is assumed to be constant and player 2 delays making risky strategy choices
until the end of the game.
12
Figure 3- The Expected Payoff’s to Player 2, given that a Successful Risky Investment is made in The First Move of
the Game
Expected Payoff given 'x' Safe Strategy Choices
$900.00
$800.00
Expected Payoffs
Scenario 2
$700.00
$600.00
Expected Payoffs
Scenario 1
$500.00
$400.00
$300.00
$200.00
$100.00
$0.00
0
1
2
ˆ =2.4
x*
3
x*= 4
5
6
V. Conclusions
The intention of this paper was to provide some theoretical evidence as to why microfinance
institutions may have abandoned the group solidarity lending practices. In understanding the
underlying reasons for change in these lending practices, it can be determined whether group lending is
still possible under alternative incentive schemes that allow the microfinance institutions to provide
continued credit outreach to those living in poverty. The theoretical models employed, in tandem with
the assumptions made in this study, indicate that the current structure of the group solidarity lending
mechanism is not sustainable in the long-term. The leveraging of the social connections within a
collective society by the Microfinance institution can be the same tool used by the borrowing group to
collude against the institution. Through a collective mentality the borrower group perfects their game
strategy in order to maximize their expected payoffs. In some circumstances, the perfected play that
maximizes their payoffs involves risky investment choices that minimize the probability of loan
repayment. The initial positive results touted by the microfinance community, quite possibly simply
represent the first stages of a new game, where the borrowers are just learning the potential outcomes of
the game by playing strictly according to the rules of engagement set down by the microfinance
institutions. The results from the model presented in this paper, under the group collusion assumption
and the assumption that the expected value of the risk investment is greater than the safe one (i.e.,
), show that over the - round 2-player sequential microfinance game, players can maximize
their expected payoffs by playing “a risky strategy at some point during the game”. And when the
number of risky action choices increase, the probability of default on loan repayments increases.
Furthermore, if risky actions are employed early on and the game does not end, the expected payoff
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from choosing the risky strategy in the future also increases relative to playing it safe. As repayment
rates decline, the microfinance institution perforce must play their “no group loan” action choice
(Figure 1).
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