Dynamic Volunteer's Dilemmas, Unique Bid Auctions, and Discrete Bottleneck Games: Theory and Experiments

Abstract

The main theme of my dissertation is the analysis of several interactive decision making situations with multiple decision makers whose interests do not fully coincide. Non-cooperative game theory is invoked to carry on this analysis.The first chapter describes an experimental study of volunteer's dilemmas that evolve over time. Only a single volunteer is required for the public good to be provided. Because volunteering is costly, each prefers that some other players bear the full costs of volunteering. Reflecting on the observation that in many naturally occurring social dilemmas it is beneficial to volunteer earlier than later, I assume that the payoff to the volunteer and the (higher) payoff to each of the non-volunteers decrease monotonically over time. I derive symmetric and asymmetric subgame perfect equilibria. The experimental results provide little support to asymmetric equilibria in which only a single subject volunteers immediately. In comparison to the symmetric subgame perfect equilibrium, they show that subjects volunteer, on average, earlier than predicted.The second chapter explores a new type of online auction, called the unique bid auction, that has recently emerged on the Internet and gained widespread popularity in many countries. In a sharp contrast to traditional auctions, the winner in this class of auctions is the bidder who submits the lowest (highest) unique bid; all ties are discarded. I propose an algorithm to numerically compute the symmetric mixed-strategy Nash equilibrium solution and then conduct a series of experiments to assess the predictive power of the equilibrium solution. The experimental results show that the solution accounts quite well for the subjects' bidding behavior on the aggregate level, but not on the individual level.The last chapter proposes a discrete version of William Vickrey's model of traffic congestion on a single road with a single bottleneck. In my model, both the strategy space and number of commuters are finite. An algorithm similar to the one used in the second chapter is proposed to numerically calculate the symmetric mixed-strategy Nash equilibrium. The discrete model is then compared with the original continuous model of Vickrey in terms of the equilibrium solution and its implications.