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.

Santrauka

Žaidimu teorijoje agentai turi galimybe sudaryti isipareigojančius susitarimus. Agentai, kaip yra mano‐ma, numato savo strategijas riboto racionalumo salygomis. Strateginiu žaidimu sritis sudaro galimybe agentui suvokti optimalios elgsenos krypti. Straipsnyje tyrinejamas ryšys tarp skirtingu žaidimu teo‐rijos sričiu tuo atveju, kai susitarimuose dalyvauja trys agentai. Atskleidžiamas neišvengiamas agentu elgsenos nesuderinamumas del riboto racionalumo, apgavysčiu bei aplinkos pokyčiu. Straipsnyje aiš‐kinama, kad žaidimu teorijos numatomos agentu susitarimu taisykles turetu būti modifikuotos siekiant ivertinti papildomu susitarimu alternatyvu galimybe.

Keywords:

• coalition games
• network games
• allocation rules
• Myerson‐value
• time‐inconsistency
• outside option
• supply chain cooperation

Reikšminiai žodžiai:

• susitarimai žaidimu teorijoje
• tinklu žaidimai
• susitarimu taisykles
• nesuderintas laikas
• papildoma alternatyva