Gradualism and Irreversibility

Jonathan Thomas, Ben Lockwood

Research output: Contribution to journalArticlepeer-review


This paper considers a class of two-player dynamic games in which each player controls a one-dimensional action variable, interpreted as a level of cooperation. The dynamics are due to an irreversibility constraint: neither player can ever reduce his cooperation level. Payoffs are decreasing in one's own action, increasing in one's opponent's action. We characterize efficient symmetric equilibrium action paths; actions rise gradually over time and converge, when payoffs are smooth, to a level strictly below the one-shot efficient level, no matter how little discounting takes place. The analysis is extended to incorporate sequential moves and asymmetric equilibria.
Original languageEnglish
Pages (from-to)339-356
Number of pages18
JournalReview of Economic Studies
Issue number2
Publication statusPublished - Apr 2002


  • cooperation
  • repeated games
  • gradualism
  • irreversibility
  • public goods


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