Bidirectional constraint satisfaction in rational strategic decision making

Abstract

We describe the properties of a constraint satisfaction network that is able to reason and decide rationally in strategic games. We use the structure of Bidirectional Associative Memory (BAM), a minimal two-layer recurrent neural network, and assume that network layers represent self and other strategies, whereas connection weights encode best responses. We apply BAM to finite-strategy two-player games, and show that network activation in the long run is restricted to the set of rationalizable strategies. The network is not guaranteed to reach a stable activation state, but any pure strategy profile that constitutes a stable state in the network must be a pure strategy Nash equilibrium. We illustrate the properties of the network using the traveler’s dilemma, the rock–paper–scissors game, and coordination games. The network’s behavior also depends on starting activation states, and we show how biases in these starting states can resolve equilibrium selection problems. Strategic decision making is a key part of complex social behavior, and our results illustrate how bidirectional constraint satisfaction networks can perform rational computations in this domain.