The distinction between parametric and strategic choices, and other tales ...
From Ben's Writing
A paper for Philosophy 3411 - Game Theory [Fall 04]
Write a 500-word encyclopedia article which explains the following concepts: a) the distinction between parametric and strategic choice, b) conflict, coordination and mixed motivity, c) the relationship between pareto superiority/inferiority/optimality and Nash equilibria, d) prisoners' dilemma, chicken, and battle of the sexes, e) divisible and indivisible cooperative dividends and the relationship between prisoners' dilemma and chicken, and f) the relationship between paretianism and proto-chicken.
In every type of game, we, as agents, have choices. These choices come in two flavours, parametric and strategic. The distinction between these two choices is simple, a parametric choice is one based on entering a fixed or constant world. This type of choice is conceptually the simpler of the two to make, as all the variables involved in it are plainly visible — of course, in practice, it can still be a difficult one to make. The second type of choice is the strategic one. This choice arises in games of pure conflict, like chess, they are also present in games of coordination, like which side of the road we should drive on, and finally, they can be found in games of mixed-motivity, such as Prisoners' Dilemma (PD), Chicken and Battle of the Sexes. These types of choices are dependant on the other agents in the game, and for this reason are the most complex. Even in games like chess, where their previous decisions are logged and up for display, there is still the uncertainty associated with the existence of a non-static world.
While we are on the topic of mixed-motivity, let us expand on the games listed above. PD, to me at least, is the most interesting. It is probably because it challenged my intuition about the situation. In a PD, two agents have been caught for some heinous crime. They are presented with two choices. Either they rat on their comrade and get a lessened sentence for their troubles, or they can bite their tongue and keep quiet. The sentencing structure goes a little like this: If both agents rat, they each get 3 years; if both keep quiet, they each get 2; and if one rats and the other keeps quiet the rat goes free while the quiet one gets five years.
The second game, Chicken, is borrowed from the rebel sub-culture of '50s. This game, again, concerns itself with two agents going head to head. This time, however, they are situated in two beefed-up muscle cars pointed at each other on some lonely stretch of country road. The game is played by applying pressure to the accelerator and speeding towards each other until one agent chickens-out. As the story goes, the winner gets to keep the other's oil pan and, of course, the chick.
The final game is the Battle of the Sexes. This game stars a pair of star struck lovers out on the town looking for a good movie. The problem, of course, is that one would rather watch their selection than the other; however, they would rather watch the movie together, than apart. This game need not be restricted to movie watching endeavours, nor, for that mater, sexes; it is simply, like the others, just figurative.
When engaged in games of mixed-motivity, there exist, sometimes, a benefit to cooperating with your opponent. This benefit is known as the cooperative dividend, and like the types of choices listed above, it too comes in two flavours. First, there is the divisible cooperative dividend; as the name implies, the agents of a game can optionally split this dividend between themselves. For an example of this, let us look at a PD. The sentences are divisible, so if it were that the agents cooperated to get 2 years each one then might still be better off, depending on the results of the bargain that enabled them to get to mutual-cooperation from mutual-defection. The second type of dividend, the indivisible one, can be seen the Deer Hunter Paradox, in the form of the bullet in the chamber of the gun. The bullet can hardly be spilt in two and still be useful. Therefore, once again, there are decisions to make.
As spoken to above, when we play games we have make decisions in them, and as such, it would be good to have some method of distinguishing between good and bad choices. This classification is done by comparing the pareto-efficiency of all the possible solutions. A solution S to a game G is pareto-superior to a solution T iff no agent prefers T to S. In this case, then, T is pareto-inferior to S, and if for all remaining solutions there exists no solution pareto-superior to S, then S is pareto-optimal. Nash's equilibrium, in these terms, becomes a solution N to G in which an agent's position is pareto-superior to any he might otherwise adopt, given that the other agents are committed to their positions.
