Balancing risk and reward: CFRRA for extensive-form games

In the field of game theory, rationality has traditionally been equated with the maximization of expected payoffs. However, in real-world scenarios, players often have different degrees of risk aversion, requiring a more suitable approach. This paper proposes the novel concept of leafset according to the concept of information set. Furthermore, we introduce Risk-Averse Equilibrium (RAE), a equilibrium that accounts for players’ risk preferences by considering both expected utility and variance. We prove the existence of RAE and modify the utility function. Based on the Counterfactual Regret Minimization (CFR) algorithm, we introduce a variant of CFR called CFRRA (Risk-Averse) algorithm, which extends the traditional CFR to address the risk in the extensive-form games (EFGs) by the risk utility function. We show CFRRA converges to approximate RAEs through experiments in different EFGs such as Kuhn Poker and Leduc Poker, highlighting its potential in managing risk in multi-agent systems.