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Developing a Game Model of a Multi-Agent Environment with Varying Degrees of Agent Competitiveness

Joon Sung Park, Bryce Wiedenbeck

Some people are competitive, some are not. As vague as its definition in colloquial settings may be, the concept of competitiveness is not foreign to us. We can roughly imagine how a competitive person would act, pick out those who are relatively more competitive, and ponder whether our society encourages competitive behavior. Indeed, that some people are more competitive than others is something many of us would agree with. But if we can more precisely understand competitiveness beyond our colloquial understandings and map out its consequences, we may be able to provide richer context to our study of competitions. Given a game, would a competitive agent thrive over those who are less competitive? How would the utilities distribute when some agents are more competitive than the others? Would an environment with more competitive agents incur better equilibrium than an environment with less competitive agents?

We have set out with the goal of creating an agent-utility model that would encapsulate varying degree of competitiveness in a given agent to answer the above questions. Agent-utility model, originating from the field of economics game theory, attempts to express agent's decision making in a mathematical expression. Throughout the summer, we developed a model that may answer our current discourse, and studied its behaviors via Gambit software through calculating various Nash equilibria, the solution concept to the model in which no agent can gain greater utility by unilaterally changing his or her strategy.

Our work done this summer is a work in progress with rooms for improvements, but we have come across interesting results that are worth mentioning. As a preliminary step of exploring our model, we observed agent behaviors in an environment where all agents are hyper competitive, and also in an environment where all agents are only mildly competitive. In both environment, we observed that agents who lack talent tend to give up before others when the cost of effort rises.

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