A non-cooperation result in a repeated discounted prisoners` dilemma with long and short run players

Abstract

This study presents a modified version of the repeated discounted prisoners'dilemma with long and short-run players. In our setting a short-runplayer does not observe the history that has occurred before he was born,and survives into next phases of the game with a probability given by thecurrent action profile in the stage game. Thus, even though it is improbable,a short-run player may live and interact with the long-run player forinf,nitely long amounts of time. In this model we prove that under a mildincentive condition on the stage game payos, the cooperative outcome pathis not subgame perfect no matter how patient the players are. Moreover withan additional technical assumption aimed to provide a tractable analysis, wealso show that payos arbitrarily close to that of the cooperative outcomepath, cannot be obtained in equilibrium even with patient players.

Bu calsma uzun ve ksa donemli oyuncularla oynanan tekrarl iskontoedilmis tutuklu acmaz oyununun degisiklik yaplms halidir. Bu calsmamzda,ksa donem oyuncu dogmadan onceki gecmisi gozlemlemiyor ve oyunun birsonraki tekrar icin hayatta kalabilme ihtimali o periyottaki aksiyon pro-li tarafndan belirleniyor. Bu suretle, mumkun gorunmesede ksa donemoyuncu sonsuz zaman diliminde hayatta kalabilir ve uzun donem oyuncuylaoyunu oynayabilir. Bu modelde, periyot getirileri uzerine bir varsayim altnda,oyuncularn sabr seviyelerinden bagmsz olarak isbirlikci sonuc gidishatnnalt oyun tam Nash dengesi olmadgn ispatladk. Ayrca, analizimizi kolaylastrmay saglayan teknik bir varsaym ile, sabrl oyuncularla bile isbirlikcisonuc gidishatnn sagladg getirilere rastgele yakn olan getirileri dengedeelde edemedigimizi gosterdik.