Amnon Rapoport, Hironori Otsubo, Bora Kim, and William E. Stein. "Unique Bid Auctions: Equilibrium Solutions and Experimental Evidence" Last revised: May 2008. Currently under review. [Manuscript]

Abstract: Two types of auction were introduced on the Internet a few years ago and have rapidly been gaining widespread popularity. In both auctions, players compete for an exogenously determined prize by independently choosing an integer in some finite and common strategy space specified by the auctioneer. In the unique lowest (highest) bid auction, the winner of the prize is the player who submits the lowest (highest) bid, provided that it is unique. We construct the symmetric mixed-strategy equilibrium solutions to the two auctions, and then test them in a sequence of experiments that vary the number of bidders and size of the strategy space. Our results show that the aggregate bids, but only a minority of the individual bidders, are accounted for quite accurately by the equilibrium solutions.

Hironori Otsubo and Amnon Rapoport. "Dynamic Volunteer's Dilemmas over a Finite Horizon: An Experimental Study" Forthcoming in Journal of Conflict Resolution. [Data & Instructions]

Abstract: Volunteer’s dilemmas that evolve over time are presented and modeled as non-cooperative n person games in extensive form with symmetric players, discrete time, finite horizon, and complete information. Volunteering is costly thereby giving rise to free riding. Reflecting on the observation that in many naturally occurring social dilemmas it is beneficial to volunteer earlier than later, our model assumes that the payoff to the volunteer and the (higher) payoff to each of the non-volunteers decrease monotonically over time. We construct symmetric and asymmetric subgame perfect equilibria to the game. An experimental study shows that financially motivated subjects who are rewarded contingent on their performance volunteer more readily when the cost of volunteering is relatively low; that they largely fail to coordinate on any of the asymmetric equilibria in which only a single subject volunteers immediately; that they volunteer, on average, earlier than predicted; and that they vary considerably from one another in their inclination to free ride.

Hironori Otsubo and Amnon Rapoport. "Vickrey's Model of Traffic Congestion Discretized" Forthcoming in Transportation Research Part B.

Abstract: Vickrey’s seminal analysis of urban traffic congestion assumes a continuum of commuters acting selfishly and a continuous strategy space. We propose a discrete version of his model that assumes a finite number of commuters and a discrete strategy space. We then present an algorithm for numerically computing a symmetric mixed-strategy equilibrium solution for the discrete model and compare it with the deterministic equilibrium solution for the continuous model due to Arnott, de Palma, and Lindsey (1990). We report significant discrepancies in travel costs and distributions of departure time between the two solutions that slowly decrease as the number of commuters increases. We then propose and exemplify two extensions of the discrete model that allow for an uncertain number of commuters and an alternative mode of transportation not subject to congestion.