This dissertation consists of two essays in Game Theory with Incomplete Information. The common theme of the essays pertains to the interpretation and origin of incomplete information in strategic situations.
In the first essay, I study bargaining between a buyer and a seller when the buyer can invest in generating outside options at a cost, and the seller cannot observe his investment choice. I model the negotiation phase as an incentive compatible and ex-post individually rational direct mechanism, which maximizes a weighted average of the buyer's and seller's expected payoff. When the weight on the buyer is larger, trade happens with certainty, the price equals the seller’s cost, and the buyer does not invest in generating outside options. When the weight on the seller is larger, the optimal mechanism is a posted price mechanism at the worst outside option that the buyer could have, provided that the cost function of the buyer is decreasing in first order stochastic dominance. The probability of trade is strictly below 1, even if it would be socially efficient to trade.
In the second essay, I propose a notion of Rationalizability, called Incomplete Preference Rationalizability, for games with incomplete preferences. Under an appropriate topological condition, the incomplete preference rationalizable set is non-empty and compact. I argue that incomplete orderings can be used to model incomplete information in strategic settings. Drawing on this connection, I show that in games with private values the sets of incomplete preference rationalizable actions, of belief-free rationalizable actions (Battigalli et al., 2011, Bergemann and Morris, 2017), and of interim correlated rationalizable actions (Dekel et al., 2007) of the universal type space coincide.
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/46367 |
| Date | 16 June 2023 |
| Creators | De Magistris, Enrico |
| Contributors | Lipman, Barton L. |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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