Book
Three essays on stochastic stability
Dissertation Abstracts International, ProQuest Information and Learning
2012
Abstract
The first chapter examines a dynamic process of unilateral and joint deviations of agents and the resulting stochastic evolution of social conventions in a class of interactions that includes normal form games, network formation games, and simple exchange economies. Over time agents unilaterally and jointly revise their strategies based on the improvements that the new strategy profile offers them. In addition to the optimization process, there are persistent random shocks on agents' utility that potentially lead to switching to suboptimal strategies. Under a logit specification of choice probabilities, we characterize the set of states that will be observed in the long-run as noise vanishes. We apply these results to examples including certain potential games and network formation games, as well as to the formation of free trade agreements across countries.
The second chapter examines an evolutionary model in which the mutation rate varies with the strategy. Bergin and Lipman (1996) show that equilibrium selection using stochastic evolutionary processes depends on the specification of mutation rates. We offer a characterization of how mutation rates determine the selection of Nash equilibria in 2x2 symmetric coordination games for single and double limits of the small mutation rates and the large population size.
The third chapter examines stochastic stability with players obeying prospect theory. We extend Young's evolutionary bargaining model to a two-stage Nash demand game in which Player 1 chooses whether to exercise an outside option in the first stage, and Players 1 and 2 play the Nash demand game in the second stage which will be reached only if the option is not exercised. In this game, the option value naturally serves as the reference point for Player 1. The stochastically stable outcomes have these properties: (i) there exists a threshold option value such that Player 1 will be better off compared to the expected utility case if the option value is at least the threshold, and worse off otherwise, (ii) the threshold level is less than half of the pie, and (iii) the stochastically stable outcome is close to the prospect theory Nash bargaining solution defined in this chapter.
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Details
- Title
- Three essays on stochastic stability
- Creators
- Ryoji SawaWilliam H SandholmMarzena RostekMarek WeretkaRicardo Serrano-PadialBenedek ValkoThe University of Wisconsin - Madison. Economics
- Series
- Dissertation Abstracts International
- Publisher
- ProQuest Information and Learning; Ann Arbor, Mich
- Number of pages
- 1 online resource (127 pages).
- Resource Type
- Book
- Language
- English
- Academic Unit
- Economics (School of Economics)
- Identifiers
- 9781267334862; 126733486X; 991021807100204721