You have always been an obedient citizen; prompt to your duties, paying your taxes and voting for representatives, who you know that were not reciprocating your righteousness. In particular, you always suspected that they were corrupted and taking side-payments, but only recently scandals broke out highlighting the extent of corruption.
In addition, your politicians exerted minimum effort governing the country and its economy which has led the country to the brink of economic collapse. (This is not to say that they were the only at fault for the state of current economic affairs, but let's take the assumption that the biggest share of the blame is attributed to them.)
Assuming there is still some margin for saving the country, how would you react to this crisis? Would you (as part of the people) sigh "bygones are bygones" and make your best to save the economy? Or, would you be bitter about the inability of those in charge, which would lead you to act in a way such that the collapse is unavoidable?
In other words, would you forget about the poor effort of those in charge and do your best? Or would you feel that you (as a citizen) were treated unfairly and try to reciprocate "the love".
Let's simplify the analysis (by making it more complex). We have the following stage game, which is a modified Prisoner's Dilemma.
The row player is the Government, which can either exert "High" or "Low effort". The column player is the Citizen, who can "Cooperate" (for example pay his taxes), or "Don't cooperate" (for example cease filling his tax form, having dealings in the underground economy, and etc.).
It's immediately obvious that Low effort and Cooperate are dominant strategies for the Government and the Citizen respectively. So, the "best prediction" about the outcome a game theorist can make is that the Government will put minimum effort in, but the citizens will still cooperate. This is the unique Nash equilibrium of this simple game, where the Government has a payoff of 4X and the Citizen 2X. Indeed this a rational outcome, in the sense that a player should always be self-interested, and choose rationally the strategy that maximizes his payoff.
The only problem with this prediction is that it exemplifies the omission from "traditional" non-cooperative game theory, the fact that in real-world people are not cold-blooded players who act without regard to the other's actions and how they deem those actions. Allow me to be more specific, all of us have emotions to which we act upon. For example, as Matthew Rabin (1993) argues if we deem the action of the other player as unfair and unkind then we might want to reciprocate with an action that is unfair and unkind, so that we will fell that social justice has been implemented.
Such an implementation of social justice can bring about outcomes that are ex ante Pareto dominated by others (strictly speaking about the bi-matrix payoffs). Indeed in the simple game above, the outcome "Low effort, Don't" is a fairness equilibrium as per Rabin (1993). Although, ex ante the Nash equilibrium "Low effort, Cooperate" seems to Pareto dominate the "Low effort, Don't", it's possible that citizens feel that their politicians were unkind to them, and as a retaliation they responded with ceasing to cooperate.
Specifically, as with the Nash equilibrium, examination of Rabin's fairness equilibrium is concerned (only) with the strategies that occur with positive probability in equilibrium. More importantly though, in Rabin's world players are concerned with reciprocity.
In particular, if a player perceives a behaviour as kind, then she might want to reward it by being kind as well, whereas an unkind behaviour might be punished. An unkind behaviour towards player i would of course lower i's material payoff. Retaliating unkindness often entails actions that lower i's material payoffs even more. Yet the satisfaction of "revenge" is possible to compensate i such that she finds it worthwhile to punish the unkind opponent. With some (heavy) abuse of notation, the payoff function of player i is
where the first term represents the material payoffs (see table), the term outside the squared brackets is the perception of j's kindness by i (if it's positive then j is perceived as kind, if it's negative as unkind and if it's 0 then j is neither). Finally, the term is inside the brackets is i's kindness.
In this framework it can be shown if the citizens expect their politicians to exert low effort, and the politicians expect the citizens to not cooperate, then "Low effort, Don't" is a fairness equilibrium.
This is far from thorough analysis of the above game, but merely a novel description. However, the main message is that behavioural game theory can help explain what traditional game theory cannot. This (extremely) simple game was devised with the "refuse" of Greeks to silently and blindly accept the idiom "bygones are bygones" to cooperate with their politicians and Troika to get out of the crisis in mind. Had they initially cooperated and avoided some costly strikes then the situation might have been better. Hence, to an outside observer not cooperating is a dominated strategy, and it seems inconceivable that the people refuse to count their losses and move on. However, as argued above behavioural game theory makes sharp predictions that it may well be that we get an equilibrium where the people just don't want to cooperate, because they want to punish the politicians; granted they do punish themselves as well, but they do punish the politicians as well.
All in all, even though the above passage by no means suggests that the simple game describes the real world, it says that there exists at least one fairness equilibrium which to my eyes seems to be pretty close to reality.
References:
Matthew Rabin. Incorporating fairness into game theory and economics. American Economic Review, 83(5):1281–1302, December 1993.
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