Communication, Beliefs, and Revenue Bounds

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This award funds three research projects in game theory. The first analyzes strategic situations in which participants communicate freely, including making statements with no strategic motives. The second project seeks to develop new methods for determining which equilibrium results are consistent with specific concepts of consistency. The third project analyzes how a profit-maximizing multi-product monopolist will choose a marketing strategy when it has incomplete information about demand. The goal here is to develop bounds on the maximum possible sales, which could provide some insight into why such firms frequently bundle goods. The results of these projects may create new tools for analyzing bargaining, negotiation, and repeated market interactions.The first project analyzes a model without the common explicit enumeration of all possible actions for the players; in practice this limits communication possibilities. Instead the PI develops a model in which players are able to freely announce their private information. Using a new refinement of sequential equilibrium, the resulting outcomes are often stable in the Kohlberg-Mertens (1986) sense. The second project presents an argument that normal form perfection, rather than backward induction or sequential equilibrium, captures the decision-theoretic consequences of dynamic consistency in games. The researcher then develops an equilibrium-based analog of rationalizability to address the issues of invariance. This means that invariance is sought as a result rather than being imposed as an axiom. The third project tackles a complicated problem in multi-dimensional optimal mechanism design. While there are no known methods for providing useful characterizations of the solution, in practice we observe that firms use simple mechanisms. The project will examine whether good revenue bounds can explain the wide use of these mechanisms.