Attractiveness maximization, risk strategies, and risk strategy equilibrium in repeated agent interactions

One of the key properties defining an intelligent agent is social ability. This means that an intelligent agent should be able to interact with other agents or humans. Before designing an intelligent agent for any multi-agent system, we need to first understand how agents should behave and interact in that particular application. In multi-agent systems, agents often need to make decisions, especially under uncertainty. When a decision-maker needs to choose among a number of choices, each having a certain probability to happen, one of the traditional ways discussed in economics is to calculate the expected utility of each choice and choose the one with the maximum expected utility. However, most of the humans do not do so in real situations. Very often, humans choose a choice with a lower expected utility. One of the famous examples is the Allais paradox. The reason why most of the people do not maximize the expected utility is that people have different attitudes towards risk in different situations and people are generally risk-averse. To model this human behavior, we propose another way of decision-making, called attractiveness maximization. In this model, every choice has an attractiveness, which is calculated from the risk attitude of the decision-maker, probability, and utility. In making decisions, decision-makers choose the choice with the maximum attractiveness. Using attractiveness maximization, the phenomenon that human do not maximize expected utility can be explained. We also find some properties of the model of attractiveness maximization, which match the human behaviors. One way to understand how agents should behave in a particular application is to model the application as a game. Besides, many real-life situations can be modeled as games. So, we extend the model of attractiveness maximization and apply the extended model to strategic games and infinitely repeated games. In strategic games, we define risk attitude and reputation, which are factors that decision-makers take into account in making decisions. We transform a strategic game to a risk game. We propose a new kind of strategies, called risk strategies. In the transformed risk game, we find a new kind of equilibrium, called risk strategy equilibrium. We also find out some properties of risk strategy equilibrium. In addition, we find that players can obtain higher payoffs in risk strategy equilibrium than in pure strategy Nash equilibrium. In infinitely repeated games, we also give definitions to risk attitude and reputation. As art infinitely repeated game is a repetition of a constituent strategic game, we transform each single round of an infinitely repeated game as a risk game. We extend the definitions of risk strategies and risk strategy equilibrium to infinitely repeated games. We also research some properties of risk strategy equilibrium and show that players can obtain higher payoffs in risk strategy equilibrium than in pure strategy Nash equilibrium. We develop several applications of attractiveness maximization and risk strategies. First, we apply the proposed concepts to the Iterated Prisoner's Dilemma, which is widely used by economists and sociologists to model and simulate many of the human interactions. Simulation shows that agents have improved performance and are reactive as well as pro-active. Second, we construct behavioral predictors and an adaptive strategy for Minority Games, which model many real life situations like the financial market, auctions and resources competitions. Simulations show that the adaptive strategy works much better than previous models. Third, we model a resource allocation problem as a Minority Game and apply the behavioral predictors and the adaptive strategy to the resource allocation problem. Simulations also show that agents with the proposed adaptive strategy are able to make more right decisions and better resource utilization than previous work.