Chapter 1 explores the subject of randomized commitments in games. Models of commitments in game theory typically assume players make a binary decision between committing to some restriction over actions, such as limiting play to a certain pure or mixed strategy, and not committing to any such restriction. I present a model in which players commit to a probability of committing in the usual sense, which allows for a novel generalization of Schelling, 1960’s notion of fractional commitments. The model is applied to certain classes of games, namely the finitely repeated prisoners’ dilemma, concave gaves such as differential duopoly, and the travelers’ dilemma.
Chapter 2 addresses strategic uncertainty in repeated public goods games. Strategic uncertainty, commonly addressed in game theory through the concept of risk dominance, has recently been modeled in the setting of infinitely repeated prisoner’s dilemmas by Blonski et al., 2011 and Blonski and Spagnolo, 2015. I argue that this approach may be used to study international environmental agreements, modeled as repeated public goods games beginning with Barrett, 1994. I extend risk dominance to repeated public goods games through two assumptions: that countries might punish all other players or a subset of them, and that conjectures about each player’s probability of cooperating are updated in each period. Applying this solution concept to a model of climate change abatement with quadratic costs, which represents the decisionsabout individually determined national contributions that parties to the Paris Agreement make, suggests policy implications: Insisting on a consensus approach may result in emissions reduction that increase at a very low rate, but focusing on cooperation within small groups of countries that increase in numbers as trust is built up can improve the ramping up of abatement activities.
Chapter 3, coauthored with Kristian Lopez-Vargas, is concerned with auction design. We analyze three proposed formats of a reverse auction in which the buyer has access to signals of each seller’s cost. This auction is a multi-unit, pay-as-bid procurement auction with one buyer and N sellers, and the three formats are intended to use the signals to reduce the offer amounts. These designs are proposed as alternatives for the auctions of the Conservation Reserve Program (CRP) in the companion paper Cramton et al., 2019, which studies them using a laboratory experiment. We use analytical and numerical methods to characterize equilibrium predictions for each format, beginning with an analysis of the simple pay-as-bid format which has a closed-form solution. We then study a format with individual price-caps, where we study the impact of varyingthe price cap’s tightness. Last, we consider two alternative formats that rank offers using scores computed from reference prices, which are determined either exogenously, using the bidder’s cost estimate, or endogenously, using the offers of bidders with similar cost estimates. We find that the scoring format that uses exogenous references prices is effective at reducing rents without limiting participation, but that endogenous reference prices lead to bidders coordinating on a high price.