Thesis teaser: Tough behavior in repeated bargaining game. A computer simulation study.
(if you are interested please tell me to read my draft. the feedback i need is simple, pointing out what is counterintuitive, what is "hm".. because if i need jargon, i may just need to copy the whole Vega-Redondo ;)
tl;dr version (aka abstract)
This thesis ventures in putting the repeated bargaining game under evolutionary force. The reason is that in light of all the essential development of one shot bargaining game, evolutionary method and the extensive literature on Prisoner's Dilemma, little has been done for the repeated bargaining game.
Part of reason for this abandoning is that, despite having a continuum of Nash equilbria, under homogenous settings, the one shot game keens on giving us what we cherish: a stable equilibrium of fairness (50-50 division), robust to many kind of tough pertubations. However, it's true that social interaction doesn't always yield unconditional egalitarian. Hence the only way so far to justify unequal Nash equilibria is to tinker with the structure of the game before the calculation takes place, for example with the heterogenity in power, preference, need, information or focal points.
Hence, this study would like to adddress the question: Is 50-50 division still an evolutionarily stable norm when it comes to repeated interaction, even without these heterogenity assumptions? Preliminary result says no.
introduction
This thesis rests in noncooperative game theory (Nash, 1950-1951). As Myerson (1999) said, this entire branch of ”practical calculus of incentives” came into existence all because of Nash.
Game theory deals with interaction among players in a narrow context. A context is narrow when one player’s action can change the course of the whole game because players’ payoffs are sufficiently intertwined. This makes expectation matter which in turn makes the interaction strategic.
The difference between classical and evolutionary game theory (Maynard, 1982) lies in the rationality assumption of their players. Built on individual decision theory, classical paradigm carries on the legacy of strong mathematical foundation for the player: neat optimization and infinite recursive thinking of common knowledge. So they say, what is the point of a theory starting with assumptions about players that are not even close to the statistically real truth? And if the collective reality doesn’t matter, what matters?
Until now the narrative has substantially shifted from these ideal players to less demanding subjects. Just as applied economics of behavioral, experimental, neuro-economics trying to figure out a reasonable approach to modelling decision makers by adding cognitive and psychological knowledge, theorists bring evolution into game theory.
Starting from an amusing observation that nature doesn’t assume any rationality of its creatures but its solution many times becomes our definition of perfect, evolutionary game theory (EGT) offers a less pervasive way of thinking into games by replacing strict assumptions by adaptive learning and letting the iterative selection process do its job. Surprisingly, sometimes it gives us the perfect equilibrium just like in classical regime, and sometimes it leads to even stricter refinements.
Another fruitful aspect to consider is time dimension. Repeated game resembles the recursive nature of human interaction along time axis and reveals new facets of the match that are not available in one shot. As in the struggle between social-efficiency and self-advantage captured by Prisoners’ Dilemma (PD), the possibility of tomorrow makes cooperation partly be in the interest of both players. It isn’t, in one shot.
This thesis ventures in putting the repeated bargaining game under evolutionary force. The reason is that the one shot bargaining game is extensively investigated and well reviewed in the literature (Binmore et al., 2003). In cooperative game theory, Nash bargaining solution is the ultimate of what should be (1950). In noncooperative, the game is already put under stochastic process (Young, 1998), evolutionary model (Binmore et al. 1998), with variations of sequential (Rubinstein, 1982), experimental (Roth, 1995),.. Despite having a continuum of NEs, under these rigorous considerations, the one shot game keens on giving us what we cherish: a stable equilibrium of fairness (50-50 division), robust to many kind of tough pertubations. However, it’s true that social interaction doesn’t always yield unconditional egalitarian. Hence the only way to push the equilibrium point to other NEs in the set is tinkering with the assumptions or structure of the game before the calculation process takes place, with the heterogenous power (Rubinstein,1982), preference, need, information or focal points (Schelling, 1980)..
In light of all these essential development, little has been done for the repeated bargaining game. Pardon my ignorance of the literature, here is the motivation and rationale of this thesis: is 50-50 division still a stable norm when it comes to repeated interaction?
Chapter 1 layouts the theoretical background on which the thesis is built on. Chapter 2 covers the literature on application of EGT on Prisoners’ Dilemma and Bargaining game. Chapter 3 deals with simulation and results. Chapter 4 concludes.