Computational & Mathematical Organization Theory, 11, 339–356, 2005 c 2006 Springer Science + Business Media, Inc. Manufactured in The Netherlands
Using an Iterated Prisoner’s Dilemma with Exit Option to Study Alliance Behavior: Results of a Tournament and Simulation STEVEN E. PHELAN RICHARD J. AREND DARRYL A. SEALE University of Nevada Las Vegas email:
[email protected] email:
[email protected] email:
[email protected]
Abstract Nearly half of all strategic alliances fail (Park and Russo, 1996; Dyer et al., 2001), often because of opportunistic behavior by one party or the other. We use a tournament and simulation to study strategies in an iterated prisoner’s dilemma game with exit option to shed light on how a firm should react to an opportunistic partner. Our results indicate that a firm should give an alliance partner a second chance following an opportunistic act but that subsequent behavior should be contingent on the value of the next best opportunity outside the alliance. Firms should be more forgiving if the potential benefits from the alliance exceed other opportunities. The strategies were also found to be robust across a wide range of game lengths. The implications of these results for alliance strategies are discussed. Keywords:
game theory, strategic alliances, opportunism, tournament
Introduction The ability to form strategic alliances has become an indispensable part of a firm’s strategic repertoire. Alliances have been used to gain quick access to resources; share knowledge, costs or risks; manage uncertainty, and enter new markets, channels, or geographies (Ernst and Halevy, 2000; Inkpen, 2001). Alliance activity has been increasing rapidly over the last twenty years with most large companies now having dozens of alliance arrangements (Ernst and Halevy, 2000; Dyer et al., 2001). Furthermore, the scope of these activities has expanded from cross-border and technology deals to include outsourcing arrangements, channel partnerships, and cross-selling agreements. It is no longer a question of whether strategic alliances work but how to make them work more effectively (Inkpen, 2001; Ernst, 2002). Despite the increasing volume of alliance activity, it has been widely reported that around 50% of strategic alliances fail (Park and Russo, 1996; Dyer et al., 2001). Various reasons have been given for alliance failure, including poor partner selection, weak strategic rationales, and ineffective alliance management (Spekman et al., 1998).
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Opportunism or “self seeking with guile” (Williamson, 1985, p. 47) has traditionally been seen as a major reason for alliance failure (Williamson, 1975; Das and Teng, 1999). The structure of an alliance often resembles an iterated prisoner’s dilemma (Parkhe, 1993; Parkhe et al., 1993), where partners have an incentive to act opportunistically in the shortterm but may learn to cooperate in repeated encounters (Axelrod, 1980; Axelrod, 1984). Thus, the study of the antecedents and consequences of opportunistic acts within an iterated prisoner’s dilemma (IPD) framework may help to understand alliance behavior. However, the IPD may not be the ideal structure to study alliances because players have no option to exit the game. The only response to opportunistic behavior by the opposing player is to also act opportunistically. Clearly, if one is unhappy with an alliance partner then termination of the arrangement may be a more prudent course of action. Similarly, the ability to exit may discipline a partner into behaving less opportunistically. One solution is to add an exit option to the game to create an iterated prisoner’s dilemma with exit option (IPDEO) game (Tullock, 1985; Vanberg and Congleton, 1992; Orbell and Dawes, 1993). Earlier studies using analytic (Arend and Seale, 2003) and experimental (Seale et al., 2004) techniques found conflicting results. However, both studies agreed that the decision to terminate an alliance relationship depends on the payoff from exiting the game (i.e. the opportunity cost of continuing to play the game). In the current study, we used an IPDEO to study alliance failure, in particular the question of how a firm should react to opportunistic behavior by its partner. We explored this question through the use of a tournament (Axelrod, 1980; Axelrod, 1984) and simulation methods (Axelrod and Dion, 1988). In general, we discovered that the top strategies were willing to give opportunistic partners a second chance but were slightly more tolerant (i.e. less likely to exit) under low opportunity cost conditions than high opportunity cost conditions. The results were quite robust over different game lengths and we were unable to use variations on the winning strategy to perturb the result. The rest of the paper examines the theory of strategic alliances and the use of games to study alliance strategy. This is followed by a discussion of the tournament and its results. The results of a series of ecological simulations aimed at improving the winning strategy in the tournament are then presented. The paper concludes with a discussion of the implications of the results for theory and practice, limitations, and directions for future research. Theoretical Background Most researchers agree that strategic alliances are a form of hybrid organization between markets and hierarchies (Williamson, 1975, 1985; Gulati, 1998). But not all hybrid organizations are strictly strategic alliances; franchises, partnerships, cartels, joint ventures, trade associations, cooperatives, and virtual organizations are also members of the same genus (Menard, 2004). Strategic alliances lie in the middle of a continuum of organizational forms somewhat toward the market end, with joint ventures more towards the corporate end (Smith, 2004). Most companies enter into strategic alliances because they expect value-enhancing synergies. Others enter into alliances because they seek to appropriate knowledge from another firm (Das and Teng, 1998). However, firms are not equally likely to form alliances. Strategic
RESULTS OF A TOURNAMENT AND SIMULATION
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alliances are more likely to occur in industries where firms are seeking speed and flexibility with deals that are typically more complex than the simple transfer of physical or financial resources, often requiring on-going access to specialized resources (Dyer et al., 2001). The complexity and open-endedness of alliance contracts makes them difficult to enforce in a court of law (Smith, 2004). The complexity and need for flexibility in the relationship means that contracts are likely to be rather incomplete, that is, without specific clauses to deal with possible contingencies (Baker et al., 2002). Also, a great deal of special regulation exists for resolving disputes in markets and corporations but very little for strategic alliances (Smith, 2004). As a result, strategic alliances are more susceptible to opportunism than other arrangements (Das and Teng, 1999). Opportunism in Alliances Opportunism incorporates a wide range of behaviors such as “lying, stealing, cheating, and calculated efforts to mislead, distort, disguise, obfuscate, or otherwise confuse” (Williamson, 1985, p. 47). As such, opportunism incorporates the economic concepts of free riding (shirking), hold up, moral hazard, adverse selection, and misappropriation of resources (stealing). Information asymmetry is at the heart of opportunism. Opportunism can be used to describe any situation where the opportunist gains because the other party to the transaction lacks the information to either alert them to the act or seek redress. Very little is actually known about the prevalence of opportunism in strategic alliances. For instance, some argue that opportunism is the predominant cause of alliance failure (Davies, 2001), while others argue that the degree of opportunistic behavior might be overstated (Hill, 1990; Das and Teng, 2000). Despite a lack of hard evidence on the prevalence of opportunism, researchers agree that the fear of opportunism raises transaction costs, that is, the costs of searching, negotiating, monitoring, and enforcing agreements (Gulati, 1995). They are also agreed that frequent interaction (direct experience), reputation, and trust decrease this fear of opportunism and lowers transaction costs (Granovetter, 1985; Gulati, 1995; Dyer and Singh, 1998).1 Drawing on the preceding insights, the growing literature on alliance management provides advice on selecting trustworthy partners, writing efficient contracts that deter opportunism, and creating an environment where trust can grow (Spekman et al., 1998; Dyer et al., 2001; Ireland et al., 2002). Partners are either known to be trustworthy on the basis of past reputation or are given the opportunity to earn trust. In the latter case, the organization is urged to institute tighter (more hierarchical) controls but this has the problem of increasing costs and lowering performance (Gulati and Singh, 1998). As such, it is assumed to be a temporary measure. This last point has led to work on the evolution of alliances (Koza and Lewin, 1998; Inkpen and Currall, 2004) and post-formation renegotiations (Reuer and Arino, 2002; Reuer et al., 2002; Arino and Reuer, 2004) that seek to adjust contracts in the light of experience. Curiously, very little has been written on how to respond to real (or perceived) acts of opportunism. One simple rule of thumb may be to terminate all alliances that involve any evidence of opportunism. However, this may leave potentially profitable deals on the table (particularly if the perception of opportunism is mistaken). The OPEC cartel, for example,
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would have broken up long ago if they automatically expelled any member of the cartel who cheated on their oil quotas. A more rational approach may be to exit when the net present value of termination exceeds the net present value of remaining in the relationship. Arend and Seale (2003) use analytical game theory to calculate whether to enter an alliance given an estimated probability of opportunism and known payoffs for entering or exiting the relationship. The Arend-Seale model has two limitations. First, it does not provide a dynamic way to update beliefs about one’s partner. Clearly, the probability of future opportunistic behavior will be conditioned by past experience. Second, the model may impose an unrealistic calculative burden on the decision maker. Since the work of Simon (1957), we know that decision makers are more likely to satisfice and use rules of thumb rather than to make decisions with sophisticated optimization algorithms. The current study seeks to discover some rules of thumb to guide the termination of alliance relationships while remaining within Arend and Seale’s (2003) game theoretic framework. Game Theory and Strategic Alliances A small but growing number of papers have used game theory to examine strategic alliance behavior (e.g. Nielsen, 1988; Parkhe, 1993; Zeng, 2003). Game theory has been defined as “. . . the analysis of rational behavior in situations involving interdependence of outcomes” (Camerer, 1991, p. 137). Interdependencies arise in a wide range of disciplines, including economics, politics and biology. The recognition that strategic alliances also give rise to interdependent outcomes has led scholars to apply game theoretic principles to the phenomenon. Most studies of strategic alliances have used the prisoner’s dilemma (PD) game to analyze alliance behavior (Parkhe, 1993; Zeng, 2003). The two strategies in the PD (cooperate or defect) are seen as akin to working towards a mutual benefit in an alliance or acting opportunistically, respectively. The payoff structure of the PD game is such that unilateral defection by one party (UD) pays more than mutual cooperation (MC), which in turn pays more than mutual defection (MD), with unilateral cooperation (UC) paying the least. Thus, UD > MC > MD > UC. Empirical evidence has been gathered to show that many strategic alliances conform to the PD payoff structure (Parkhe et al., 1993). In a one shot game, the dominant strategy is to defect, which paradoxically brings a lower payoff than if both sides cooperated. This result would suggest that the prospects for short-term alliances are poor. More interest has been devoted to the analysis of repeated, or iterated, PD games. Here game theorists have been able to demonstrate that mutual cooperation is possible, particularly when there is a ‘shadow of the future’, or the prospect of an indefinite number of future interactions (Axelrod, 1984; Axelrod and Dion, 1988). Empirical research on strategic alliances have generally confirmed that a ‘shadow of the future’ improves cooperation (Parkhe, 1993; Zeng, 2003). A number of strategies have also been investigated for playing the iterated prisoner’s dilemma (IPD) of indefinite duration. The best known strategy is tit-for-tat (TFT), which emerged as the winning strategy in two tournaments organized to find effective strategies for the IPD (Axelrod, 1980). In addition to being the simplest strategy in both tournaments,
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TFT was also nice (it never defected first), retaliatory (it punished defectors by defecting) and forgiving (it immediately reestablished cooperation once a partner stopped defecting). All of this suggests that mutual benefits can be realized in strategic alliances if we find an effective strategy for dealing with opportunistic acts (i.e. TFT). However, no study to date has investigated the prevalence or effectiveness of TFT as a strategy in strategic alliances. It is our contention that TFT will not be a viable strategy in the real world for the simple reason that companies have an option to terminate an alliance in which a partner is acting opportunistically and the available evidence suggests that alliance termination is a very common strategy (Park and Russo, 1996; Das and Teng, 2000). Game theory seeks to reduce real world messiness to a few simple principles that are analytically tractable (Parkhe, 1993). However, in this case we believe that the PD game has oversimplified alliance strategies and that TFT may not be the most effective strategy when exit is an option. The Iterated Prisoner’s Dilemma with Exit Option We model alliance activity as a repeated prisoner’s dilemma game where each player has an option to exit at the beginning of each alliance stage. We assume the standard (symmetric) PD payoff inequalities hold: UD > MC > MD > UC, and 2 MC > UD + UC (Axelrod, 1980). The standard strategies of cooperate (C) and defect (D) are available as well as an exit option (E), which we model as giving each firm a payoff of its opportunity cost (O) when played. Thus, each stage of a (symmetric) IPDEO game is represented by the following pattern of payoffs:
Firm 2 Firm 1
C
D
E
C
MC, MC
UC, UD
O, O
D
UD, UC
MD,MD
O, O
E
O, O
O, O
O, O
When the opportunity cost exceeds the payoff for mutual defection but is less than the payoff for mutual cooperation (i.e., UD > MC > O > MD > UC), a natural assumption for alliance formation2 , then the dominant strategy for each firm is to exit. Thus, game theory’s backward induction argument would predict that neither firm enters the alliance if the firms analyze the game one stage at a time. However, when prisoner’s dilemma games are repeated in time, cooperation can emerge as a viable strategy (Axelrod, 1984; Axelrod, and Dion, 1988). An earlier study used analytical techniques to calculate an optimal level of cooperation (and conversely an acceptable level of opportunism) that would provide enough incentives for partners to remain in the alliance and thus generate a solution for the IPDEO (Arend and
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Seale, 2003). This solution led to the prediction that cooperation would rationally increase with opportunity cost in order to keep both players interested in remaining in the alliance. An empirical test of the model’s predictions was also conducted by asking a number of human subjects to play the game in a laboratory setting (Seale et al., 2004). The results ran counter to the analytical prediction—subjects showed more opportunistic behavior as opportunity costs increased. As a result, we were left with an open question as to what strategy is, in fact, optimal in such an alliance model; was it a rational strategy based on optimization or an intuitive, learned strategy based on human insight, or was it something else? The current study attempts to perform another test of the model using a pair of techniques commonly utilized to explore game theoretic models. The first technique involves a round robin tournament where participants are asked to submit a potentially winning strategy to the tournament with a winner-take-all prize for the victor. According to Axelrod (1980), a tournament is a useful way to generate effective strategies because strategies are generally submitted by knowledgeable experts in the field who have been given the incentive and time to develop competitive approaches. Lab subjects, on the other hand, are often unfamiliar with the task and have little incentive or time to develop effective responses. Tournament strategies are also more transparent than the strategies of lab subjects because we are able to delve into the code of winning tournament strategies to examine their logic.3 The second approach uses a Monte Carlo simulation to test variations on the winning strategy in the hope of evolving a more robust solution. It is unlikely that the submitted tournament strategies will have an optimal solution to the game; however, the winning strategy may very well be close to an optimal solution. By systematically manipulating key elements of the winning strategy, we hoped to improve on the winning strategy and therefore develop a better understanding of how to succeed at this game, in particular, and alliances in general.
The Tournament In late 2003, members of the Academy of Management, Game Theory Society, and Strategic Management Society were issued electronic invitations to submit strategies for an iterated prisoner’s dilemma game with exit option tournament carrying a winner take all prize of $US1000. They were directed to the researchers’ website for further information. The instructions to participants are reproduced in the Appendix.
Characterization of Submitted Strategies A total of twelve strategies were received from the participants in the US, China, and Korea. Participants were invited to name their own strategies. Four additional reference strategies were added to the tournament pool, including the Arend-Seale analytical solution, tit-for-tat, random, and quick exit. A description of each strategy is presented in Table 1 below:
N
Y
Y
Y
N
Y
N
N
N
Y
Y
Arizona
Carnegie
Coop or exit
Crab
Fivecount
Foolsfinder
LastStrat
Phishing
Phoenix
Quick Exit
N
Y
Y
Y
N
Y
N
N
N
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
N
Y
N
N
N
N
Y
N
N
Y
Y
N
N
N
N
Y
Y
Y
Y
Nice Forgiving Exit path Retaliatory Contingent
Strategies in tournament.
Analytical
Strategy
Table 1.
Cooperate on every move. Exit on first defect. (Continued on next page.)
Cooperate first. Exit on the first defect in the high opportunity cost condition. Exit after three consecutive defects in the low opportunity cost condition. Defect after receiving a defect and only cooperate after three consecutive cooperates by opponent.
Opponent’s behavior is classified into 1 of 8 conditions. Generally plays tit for tat but occasionally tests opponent with defect and then attempts to reestablish cooperation. Will exit if underperforming opportunity cost after 30 or 50 rounds.
If winnings are less than 24 after six rounds then exit else repeat pattern indefinitely.
Starts with pattern {D, D, C, D, D, C}
Defect on first move and cooperate on second. If player cooperates on third move then defect every time they cooperate on the previous move. Otherwise play tit for tat. If opponent defects 3 times in a row then exit.
Cooperate on first round. If opponent defects on first round, defect on second round. If opponent defects on second round then exit. For remainder of rounds, if opponent has defected anytime in the last five rounds then defect else cooperate.
Cooperate always. Exit after 2 defects in high opportunity condition and 1 defect in low opportunity condition. Always defect until opponent defects three times then exit.
In high opportunity cost condition, exit if opponent defects; always defect on round 45 then exit.
In low opportunity cost condition, exit if opponent defects; always defect on round 235 then exit.
If opponent cooperates then cooperate
Tit for tat for first twenty rounds. Continues tit for tat unless cooperation falls to less than 30% of moves in low opportunity cost condition or 70% in high opportunity cost. Also attempts to reestablish cooperation after eight consecutive defects.
Cooperate 82.6% of the time in the high opportunity cost situation, and 23.6% of the time in the low opportunity cost situation. Exit anytime average payoff is below opportunity cost after the first 5 rounds.
Description
RESULTS OF A TOURNAMENT AND SIMULATION
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Y
Y
Y
Y
Tit for tat
Tit for tat or exit
Tit for two tats
Y
Y
Y
Y
N
N
Y
N
Y
Y
Y
Y
Y
N
N
N
Y
N
N
N
Play tit for tat but require two cooperates before resuming cooperation after a defect.
Play tit for tat but exit after two defects in high opportunity cost condition. In low opportunity cost condition, exit after three defects or when average winnings falls below opportunity cost.
Mimic your opponent’s last strategy. If opponent cooperated, cooperate. If opponent defected, defect. Never exit.
Cooperate unless the opponent defects more than twice in the last ten rounds in which case exit.
Randomly choose to cooperate, defect, or exit with uniform (equal) probability.
Description
Nice — always cooperates first, Forgiving — will cooperate after opponent defects Exit path — has capacity to exit game, Retaliatory — punishes defectors by defecting, Contingent —strategy contingent on opportunity costs
N
TenCount
Nice Forgiving Exit path Retaliatory Contingent
(Continued).
Random
Strategy
Table 1.
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RESULTS OF A TOURNAMENT AND SIMULATION Table 2.
Descriptive statistics by strategy.
Min
Actual game length as (%) of scheduled
Avg. payoff before exit
N
Rank
Avg. payoff per round
Analytical
480
12
5.60
8.00
3.15
17
5.99
Arizona
480
3
7.10
8.00
3.60
77
6.84
Carnegie
480
8
6.91
8.00
3.80
51
6.49
Coop or exit
480
5
7.01
8.00
3.80
64
6.41
Crab
480
13
5.55
7.75
3.80
9
6.26
Five Count
480
9
6.89
8.00
3.10
69
6.31
Fool’s finder
480
11
6.02
7.97
3.55
35
6.57
LastStrat
480
15
5.42
7.65
3.60
42
6.06
Phishing
480
16
5.13
7.85
3.13
42
5.65
Phoenix
480
2
7.16
8.00
3.70
70
6.77
Quick exit
480
4
7.03
8.00
3.80
64
6.48
Random
480
14
5.53
7.85
2.45
6
6.04
Ten Count
480
7
6.93
8.00
3.00
67
6.19
Tit for Tat
480
6
6.96
8.00
3.11
82
6.80
Strategy
Max
Tit for tat or exit
480
1
7.18
8.00
3.70
71
6.88
Tit for two tats
480
10
6.69
8.00
2.75
80
6.37
Overall average
7680
6.44
7.94
3.38
53
6.38
Tournament Results Each of the sixteen strategies was matched with every other strategy on thirty occasions for a total of 7,680 runs. The overall rankings of average winnings per round and average winnings before opponent exited are presented in Table 2. The average winnings per round for each strategy against each other strategy is presented in Table 3. The winning strategy was Tit for Tat or Exit (TTE), submitted by Jia-wei Li of the Harbin Institute of Technology, China, which narrowly defeated the Phoenix strategy. In general, nice strategies (including TTE and Phoenix) significantly out-performed other strategies. As a result, there was a high correlation (r = 0.74, p < 0.01) between actual game length and average payoff. Nice strategies stayed in the game longer and thus reaped higher rewards. Tit for tat (TFT), the IPD tournament winner, placed sixth in our tournament, suggesting that it was not the best strategy for the IPDEO game. Quick exit (after any defect) placed fourth. The top three submitted strategies in the tournament had several elements in common. First, they used a tit-for-tat approach. Second, they set a trigger to exit the game after a given number of defections. The actual number of defections was contingent on the opportunity cost. In a high opportunity cost environment the strategies exited sooner. When the opportunity cost was low, they waited longer before exiting. The TTE strategy also
8.00 8.00
5.45
5.45
5.62
5.47
5.53
5.59
5.48
5.46
5.45
5.50
5.32
5.47
5.47
5.18
Carnegie
Cooperate or exit
Crab
Five Count
Fool’s finder
LastStrat
Phishing
Phoenix
Quick Exit
Random
Ten Count
Tit for Tat
Tit for tat or exit
Tit for two tats
8.00
8.00
5.54
8.00
8.00
5.11
5.19
7.87
8.00
5.38
8.00
7.78
8.00
5.48
5.56
5.51
Arizona
7.76
7.76
7.76
7.76
5.57
7.76
7.76
5.87
5.60
5.60
7.76
5.60
7.76
7.77
7.76
5.63
Analytical Arizona Carnegie
Average payoffs by strategy.
Analytical
Table 3.
8.00
8.00
8.00
8.00
5.59
8.00
8.00
5.90
5.63
5.64
8.00
5.63
8.00
7.78
8.00
5.68
5.05 8.00
5.32 8.00
5.16 8.00
4.90 8.00
5.33 5.56
5.38 8.00
5.36 8.00
5.16 3.85
5.16 5.60
5.21 5.60
5.38 8.00
5.39 5.60
5.31 8.00
5.38 7.78
5.16 8.00
5.07 5.57
5.03
7.87
7.87
5.08
5.48
5.38
7.36
5.63
4.61
5.39
5.38
5.64
5.32
5.38
7.87
5.38
3.20
5.35
4.22
5.08
5.40
5.38
5.53
4.92
4.60
4.17
5.38
5.38
5.31
5.38
4.97
5.22
3.41
5.59
3.48
5.29
5.53
5.65
5.63
3.54
5.11
5.41
3.41
5.38
5.58
5.65
4.89
5.54
8.00
8.00
8.00
8.00
5.57
8.00
8.00
5.85
5.75
7.47
8.00
5.58
8.00
7.78
8.00
5.62
8.00
8.00
8.00
8.00
5.58
8.00
8.00
5.87
5.60
5.60
8.00
5.60
8.00
7.78
8.00
5.63
5.45
5.48
5.48
5.43
5.50
5.46
5.48
5.48
5.52
5.49
5.46
5.55
5.45
5.47
5.46
5.49
8.00
8.00
8.00
8.00
5.64
8.00
8.00
6.16
5.94
5.94
8.00
5.99
8.00
7.78
8.00
6.00
8.00
8.00
8.00
8.00
5.54
8.00
8.00
3.69
4.43
7.87
8.00
5.38
8.00
7.78
8.00
5.55
8.00
8.00
8.00
8.00
5.56
8.00
8.00
5.80
5.57
7.87
8.00
5.53
8.00
7.78
8.00
5.60
8.00
8.00
8.00
8.00
5.62
8.00
8.00
3.85
6.80
5.68
8.00
5.48
8.00
7.78
8.00
6.45
Cooperate Five Fool’s Quick Ten Tit for Tit for Tit for or exit Crab count finder LastStrat Phishing Phoenix exit Random count Tat tat or exit two tats
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RESULTS OF A TOURNAMENT AND SIMULATION Table 4.
Mean results by opportunity cost. Opportunity Cost
Variable
Low (4)
High (7)
t (4-7)
Prob t
Payoff per round
5.74
7.15
−178.64
