Abstract
We consider an evolutionary model of social coordination in a 2 × 2 game where two groups of players prefer to coordinate on different actions. Players can pay a cost to learn their opponent’s group: if they pay it, they can condition their actions concerning the groups. We assess the stability of outcomes in the long run using stochastic stability analysis. We find that three elements matter for the equilibrium selection: the group size, the strength of preferences, and the information’s cost. If the cost is too high, players never learn the group of their opponents in the long run. If one group is stronger in preferences for its favorite action than the other, or its size is sufficiently large compared to the other group, every player plays that group’s favorite action. If both groups are strong enough in preferences, or if none of the groups’ sizes is large enough, players play their favorite actions and miscoordinate in inter-group interactions. Lower levels of the cost favor coordination. Indeed, when the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough.
Highlights
Conventions with Costly InformationSince the seminal contribution of Kandori et al [1], evolutionary game theorists have used stochastic stability analysis and 2 × 2 coordination games to study the formation of social conventions (Lewis [2] and Bicchieri [3] are classical references on social conventions from philosophy, while for economics, see Schelling [4], Young [5], and Young [6])
When the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough
Some of these works focus on coordination games such as the battle of sexes: a class that describes situations in which two groups of people prefer to coordinate on different actions
Summary
Since the seminal contribution of Kandori et al [1], evolutionary game theorists have used stochastic stability analysis and 2 × 2 coordination games to study the formation of social conventions (Lewis [2] and Bicchieri [3] are classical references on social conventions from philosophy, while for economics, see Schelling [4], Young [5], and Young [6]). It is as if learning an opponent’s group requires too much effort, and no player ever learns it Given this scenario, Neary’s results are the same as in our analysis when the cost is high. We firstly enlarge Neary’s analysis to the case when players learn their opponent’s group at zero cost In this case, only states where all the players in one group buy the information can be stochastically stable: this result was not possible in the analysis of Neary. Comparing the high-cost case with the low-cost case enriches the previous analysis From this comparison, we can say that reducing the cost of learning the opponent’s group increases the probability of inter-group coordination in the long run. We give all proofs in the Appendix A and we give the intuition during the text
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