Abstract
This paper proposes an envy-incorporated cooperative game model and investigates the envy effects on players’ coalition-forming and payoff-allocating decisions. A player’s utility depends on her/his own payoff and the envy toward other players, inside and outside the same coalition, with higher payoffs. Envy core is defined to characterize stable coalition structures and payoff allocations of this new game. Conditions for the envy core to be nonempty are provided. The relative significance of in-coalition envy and out-coalition envy is shown to be a key factor to the form of the envy core. Application to a simple game shows that envy may significantly change players’ decisions.
Keywords: Cooperative game; core; envy; coalition; behavior
DOI: 10.3934/jimo.2017031