Robustness to Strategic Uncertainty
AbstractIn games with continuum strategy sets, we model a player’s uncertainty about another player’s strategy, as an atomless probability distribution over the other player’s strategy set. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles in which every player’s strategy is optimal under his or her uncertainty about the others. General properties of this robustness criterion are derived and it is shown that it is a refinement of Nash equilibrium when payoff functions are continuous. We apply the criterion to a class of Bertrand competition games. These are discontinuous games that admit a continuum of Nash equilibria. Our robustness criterion selects a unique Nash equilibrium, and this selection agrees with recent experimental findings.
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Bibliographic InfoPaper provided by Research Institute of Industrial Economics in its series Working Paper Series with number 910.
Length: 27 pages
Date of creation: 30 Mar 2012
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Nash equilibrium; Refinement; Strategic uncertainty; Bertrand competition; Log-concavity;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-10 (All new papers)
- NEP-COM-2012-04-10 (Industrial Competition)
- NEP-GTH-2012-04-10 (Game Theory)
- NEP-HPE-2012-04-10 (History & Philosophy of Economics)
- NEP-MIC-2012-04-10 (Microeconomics)
- NEP-UPT-2012-04-10 (Utility Models & Prospect Theory)
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