Fully mixed strategies in auction games

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Auctions have a rich history, dating back 2500 years to Babylonia, and have evolved significantly while retaining their core purpose. This thesis explores auctions as more than mere profit-maximizing tools. The introductory chapter highlights the importance of identifying auction game classes, noting that certain problems can be more effectively addressed through auction mechanisms. Chapters 2 to 4 delve into specific auction games. Chapter two introduces cost uncertainty into the Bertrand-Edgeworth competition literature, analyzing a duopoly where costs are private information. It bridges the gap between the full information Bertrand-Edgeworth model and the Bertrand under uncertainty model, revealing that firms set supracompetitive prices in a first price variable quantity auction with capacity constraints. Chapter three compares the Chicken Game and the War of Attrition Game, extending the Chicken Game into a continuous environment and demonstrating a lack of Nash Equilibrium in the continuous Chicken Game. The fourth chapter investigates a multistage model involving capacity precommitment with unknown costs, extending Kreps and Scheinkman's model. Here, firms set capacities without knowing their marginal costs, leading to asymmetric equilibria and large equilibrium quantities, with significant changes when unit costs differ.