How To Play Well in Non-Zero Sum Games: Some Lessons from the Generalized Traveler’s Dilemma

A comparison of past experimental results on the ITD and the effects on strategy performance of altering the payoff matrix.

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Abstract

We are interested in two-person games whose structure is far from zero-sum. We study the iterated Traveler’s Dilemma (TD) which is a two-player, non-zero sum game that, depending on the exact values of its critical parameters, may offer plenty of incentives for cooperation. We first briefly summarize the results of a round-robin tournament with 36 competing strategies that was motivated by the work by Axelrod et al. on the iterated Prisoner’s Dilemma. We then generalize the “default” version of Iterated TD with respect to two important game parameters, the bonus value and the “granularity” of the allowable bids. We analytically show the impact of the ratio of these two parameters on the game structure. Third, we re-run the 36-player round-robin tournament and investigate how varying the bonus-to-granularity ratio affects relative performances of various types of strategies in the tournament. We draw some conclusions based on those results and outline some promising ways forward in further investigating games whose structures seem to defy the prescriptions of classical game theory.