Deriving an optimally deceptive policy in two-player iterated games

We formulate the problem of determining an optimally deceptive strategy in a repeated game framework. We assume that two players are engaged in repeated play. During an initial time period, Player 1 may deceptively train his opponent to expect a specific strategy. The opponent computes a best response. The best response is computed on an optimally deceptive strategy that maximizes the first player's long-run payoff during actual game play. Player 1 must take into consideration not only his real payoff but also the cost of deception. We formulate the deception problem as a nonlinear optimization problem and show how a genetic algorithm can be used to compute an optimally deceptive play. In particular, we show how the cost of deception can lead to strategies that blend a target strategy (policy) and an optimally deceptive one.