Essays in Bargaining, Auctions and Payments

This dissertation studies three game-theoretical models in bargaining, auctions, and payment systems. The first chapter examines reputational bargaining when one party may possess full information about the rationality of the opponent. The model highlights the role of second-order beliefs and studies whether a fully informed player has incentives to reveal their information through a fair offer. The analysis shows that multiple equilibria can arise, including equilibria in which rational players strategically avoid revealing their information to preserve reputational advantages. The second chapter analyzes simultaneous participation in sealed-bid auctions with unit-demand bidders. Unlike standard auction models, the setting admits no symmetric pure-strategy equilibrium. The chapter establishes the existence of symmetric mixed-strategy equilibria and shows that bidders optimally place bids in all available auctions with probability one. The third chapter studies card acceptance and payment choice in a model where consumers can search for merchants that accept card payments. Despite transaction fees, sellers may optimally accept cards to attract customers. The model features multiple equilibria with different levels of card acceptance. A calibrated extension using European payment diary data is employed to evaluate policy interventions, showing that subsidies to card usage may generate unintended general equilibrium effects that reduce card adoption.