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Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy

  • Hitoshi Matsushima EMAIL logo
Veröffentlicht/Copyright: 20. November 2019
The B.E. Journal of Theoretical Economics
Aus der Zeitschrift The B.E. Journal of Theoretical Economics Band 20 Heft 1

Abstract

This study investigates infinitely repeated games of a prisoner’s dilemma with additive separability in which the monitoring technology is imperfect and private. Behavioral incentives indicate that a player is not only motivated by pure self-interest but also by social preference such as reciprocity, and that a player often becomes naïve and selects an action randomly due to her cognitive limitation and uncertain psychological mood as well as the strategic complexity caused by monitoring imperfection and private observation. By focusing on generous tit-for-tat strategies, we characterize a behavioral version of Nash equilibrium termed behavioral equilibrium in an accuracy-contingent manner. By eliminating the gap between theory and evidence, we show that not pure self-interest but reciprocity plays a substantial role in motivating a player to make decisions in a sophisticated manner.

Keywords: repeated prisoner’s dilemma; imperfect private monitoring; generous tit-for-tat strategy; reciprocity; naïveté; behavioral equilibrium
JEL Classification: C70; C71; C72; C73; D03

Acknowledgements

This research was financially supported by a grant-in-aid for scientific research (KAKENHI 25285059) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of the Japanese government, as well as by the Center of Advanced Research in Finance at the University of Tokyo. We are grateful to Yutaka Kayaba and Tomohisa Toyama for their support in drafting an earlier version of this study. All errors are mine.

Appendix

A

A Proof of Theorem 3

Since ri(c;p)−ri(d;p) is increasing and R(p) is decreasing in p , it follows from Theorem 1 that there is a unique level of monitoring accuracy pˆj∈[p_,1] that satisfies the following properties for each p∈[p_,1] ; if p<pˆj , then:

ri(c;p)−ri(d;p)<R(p),

and, therefore, wj(c;p) is decreasing in p∈[p_,pˆi] . If p>pˆj , then:

ri(c;p)−ri(d;p)>R(p),

and, therefore, wj(d;p) is increasing in p∈[pˆi,1] . These properties imply that the higher p is, the less kind opponent j is.

  Q.E.D.

B

B Proof of Theorem 4

From Theorem 2, if p<pˆi , then,

εi(p)=ri(d;p).

Since ri(d;p) is increasing in p , εi(p) is increasing in p∈[p_,pˆi] . If p>pˆi , then,

εi(p)=1−ri(c;p).

Since ri(c;p) is increasing in p , εi(p) is decreasing in p∈[pˆi,1] . From these observations and Theorem 1, we obtain the proof of Theorem 4.

                         Q.E.D.

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Published Online: 2019-11-20

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/bejte-2019-0030
Schlagwörter für diesen Artikel
repeated prisoner’s dilemma; imperfect private monitoring; generous tit-for-tat strategy; reciprocity; naïveté; behavioral equilibrium

Artikel in diesem Heft

  1. Research Articles
  2. Optimal Forestry Contract with Interdependent Costs
  3. Bi and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition
  4. Pay-What-You-Want in Competition
  5. Two Rationales for Insufficient Entry
  6. Students’ Social Origins and Targeted Grading
  7. Pricing, Signalling, and Sorting with Frictions
  8. On the Economic Value of Signals
  9. The Core in Bertrand Oligopoly TU-Games with Transferable Technologies
  10. Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly
  11. Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims
  12. Costly Rewards and Punishments
  13. Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies
  14. Strategic Activism in an Uncertain World
  15. On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy
  16. Optimal Incentives Under Gift Exchange
  17. Public Good Indices for Games with Several Levels of Approval
  18. Vagueness of Language: Indeterminacy under Two-Dimensional State-Uncertainty
  19. Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis
  20. Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy
  21. Flourishing as Productive Tension: Theory and Model
  22. Notes
  23. A Note on Reference-Dependent Choice with Threshold Representation
  24. Regular Equilibria and Negative Welfare Implications in Delegation Games
  25. Unbundling Production with Decreasing Average Costs
  26. A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution
  27. Decision Making and Games with Vector Outcomes
  28. Capital Concentration and Wage Inequality
  29. Annuity Markets and Capital Accumulation
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