Interaction and imitation in a world of Quixotes and Sanchos

This paper studies a two-population evolutionary game in a new setting in between a symmetric and an asymmetric evolutionary model. It distinguishes two types of agents: Sanchos, whose payoffs are defined by a prisoner’s dilemma game, and Quixotes, whose payoffs are defined by a snowdrift game. Cons...

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Bibliographic Details
Published inJournal of evolutionary economics Vol. 29; no. 3; pp. 1037 - 1057
Main Authors Cabo, Francisco, García-González, Ana
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2019
Springer Nature B.V
Subjects
Agents
Compliance
Economic Growth
Economic models
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Entrepreneurship
Equilibrium
Game theory
Imitation
Institutional/Evolutionary Economics
Microeconomics
Population
R & D/Technology Policy
Regular Article
Social norms
D01
Heterogeneous preferences
Q58
C73
Two-population evolutionary game
Symmetric and asymmetric games
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Summary:This paper studies a two-population evolutionary game in a new setting in between a symmetric and an asymmetric evolutionary model. It distinguishes two types of agents: Sanchos, whose payoffs are defined by a prisoner’s dilemma game, and Quixotes, whose payoffs are defined by a snowdrift game. Considering an imitative revision protocol, a revising agent is paired with someone from his own population or the other population. When matched, they observe payoffs, but not identities. Thus, agents in one population interact and imitate agents from their own population and from the other population. In this setting we prove that a unique mixed-strategy asymptotically stable fixed point of the evolutionary dynamics exists. Taking as an example the compliance with social norms, and depending on the parameters, two type of equilibrium are possible, one with full compliance among Quixotes and partial compliance among Sanchos, or another with partial compliance among Quixotes and defection among Sanchos. In the former type, Sanchos comply above their Nash equilibrium (as they imitate compliant Quixotes). In the latter type, Quixotes comply below their Nash equilibrium (as they imitate defecting Sanchos).
ISSN:0936-9937
1432-1386
DOI:10.1007/s00191-019-00620-3