TITLE:
Equilibria Immune to Deviations by Coalitions in Infinite Horizon Non-Cooperative Games
AUTHORS:
Milan Horniaček
KEYWORDS:
Coalition, Discounting, Infinite Horizon, Pareto Efficiency, Populations of Players
JOURNAL NAME:
Natural Science,
Vol.6 No.13,
August
25,
2014
ABSTRACT: Infinite horizon
discrete time non-cooperative games with observable actions of players and discounting
of future single period payoffs are a suitable tool for analyzing emergence and
sustainability of cooperation between all players because they do not contain
the last period. A subgame perfect equilibrium is a standard solution concept
for them. It requires only immunity to unilateral deviations in any subgame. It
does not address immunity to deviations by coalitions. In particular, it does
not rule out cooperation based on punishments of unilateral deviations that the
grand coalition would like to forgive. We first briefly review concepts of
renegotiation-proofness that rule out such forgiveness. Then we discuss the
concept of strong perfect equilibrium that requires immunity to all deviations
by all coalitions in all subgames. In games with only one level of players
(e.g. members of the population engaged in the same type of competitive
activity), it fails to exist when the Pareto efficient frontier of the set of
single period payoff vectors has no sufficiently large flat portion. In such a
case, it is not possible to punish unilateral deviations in a weakly Pareto efficient
way. In games with two levels of players (e.g. members of two populations with
symbiotic relationship, while activities within each population are
competitive), it is possible to overcome this problem. The sum of benefits of
all players during a punishment can be the same as when nobody is punished but
its distribution between the two populations can be altered in favor of the
punishers.