# Formalizing Risk Strategies and Risk Strategy Equilibrium in Agent Interactions Modeled as Infinitely Repeated Games

## Abstract

To design intelligent agents for multi-agent applications, like auctions and negotiations, we need to first analyze how agents should interact in these applications. Game theory is a tool, which can be used. In game theory, decision-making often depends on probability and expected utility. However, decision makers usually violate the expected utility theory when there is risk in the choices. Instead, decision makers make decisions according to their attitudes towards risk. Also, reputations of other agents in making certain actions also affect decision-making. In this paper, we make use of risk attitude, reputation and utility for making decisions. We define the concepts of *risk strategies*, *risk strategy equilibrium*, and a formalized way to find the risk strategy equilibrium in infinitely repeated games. Simulations show that players get higher payoff by using risk strategies than using other game theoretic strategies.

## Keywords

Nash Equilibrium Game Theory Mixed Strategy Pure Strategy Intelligent Agent## Preview

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