# Playing Challenging Iterated Two-Person Games Well: A Case Study on the Iterated Traveler’s Dilemma

A further study of the Iterated Traveler’s Dilemma, with some tweaks and additions to strategies in the tournament.

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## Abstract

We study an interesting 2-player game known as the Iterated Traveler’s Dilemma, a non-zero sum game in which there is a large number of possible actions in each round and therefore an astronomic number of possible strategies overall. What makes the Iterated TD particularly interesting is that it defies the usual prescriptions of classical game theory insofar as what constitutes an “optimal” strategy. In particular, TD has a single Nash equilibrium, yet that equilibrium corresponds to a very low payoff, essentially minimizing social welfare. We propose a number of possible strategies for ITD and perform a thorough comparison via a round-robin tournament in the spirit of Axelrod’s well-known work on the Prisoner’s Dilemma. We motivate the choices of “players” that comprise our tournament and then analyze their performance with respect to several metrics. Finally, we share some interesting conclusions and outline directions for future work.

## Keywords

game theory, two-person non-zero-sum games, bounded rationality, decision making under uncertainty, tournaments