Allocation rules with outside option in cooperation games with time-inconsistency

Abstract

In game theory agents have the possibility to make binding agreements. The agents are assumed to determine their strategies based on intended but bounded rationality. The field of strategic games provides the possibility to an agent to understand the optimality of his behaviour. In coalition and network games stability, Pareto-efficiency and fairness of agreements is investigated. The paper shows the relationship between the different fields of game theory in the case of 3 agents. On that basis it shows the ubiquity of time-inconsistency in dynamic setting due to bounded rationality, deception and environment changes. The paper explains why allocation rules like the Shapley-based Aumann-Drèze-value and the Myerson-value for coalition structures must be modified in dynamic setting in order to consider the influence of excluded agents, the outside option. An accordingly modified allocation rule is introduced and investigated. It is shown that the “Aumann-Drèze-value” and the “Myerson-value for coalition structures” remains relevant for the case that the switching of the partner is connected with high costs. It is shown through the example of enterprise cooperation in supply chains that low partner switching costs require the introduced allocation rule that considers the outside option.

Žaidimų teorijoje agentai turi galimybę sudaryti įsipareigojančius susitarimus. Agentai, kaip yra manoma, numato savo strategijas riboto racionalumo sąlygomis. Strateginių žaidimų sritis sudaro galimybę agentui suvokti optimalios elgsenos kryptį. Straipsnyje tyrinėjamas ryšys tarp skirtingų žaidimų teorijos sričių tuo atveju, kai susitarimuose dalyvauja trys agentai. Atskleidžiamas neišvengiamas agentų elgsenos nesuderinamumas dėl riboto racionalumo, apgavysčių bei aplinkos pokyčių. Straipsnyje aiškinama, kad žaidimų teorijos numatomos agentų susitarimų taisyklės turėtų būti modifikuotos siekiant įvertinti papildomų susitarimų alternatyvų galimybę.