Economics game theory paper - Essay Example

Rationality is the first basic assumption of consumer behaviour in microeconomic theory. The implication of rationality is that the consumer’s decisions are motivated by the pursuit of maximizing his/her own utility. In the context of long term health insurance, the rational consumer’s objective is to maximize his utility over the long run by insuring against possible utility losses resulting from ailments. Therefore, if the consumer is rational, under certainty, that is if the consumer knew the exact health contingencies that will occur, the purchase will be made only if the resulting long run utility of the purchase is (weakly) greater than the long run utility of the consumer if he/she does not make the purchase.

However, what complicates the situation is that the occurrence of some event that causes damage to health is random and the consumer does not know whether it will occur or not at the time of making the purchase. Therefore, the consumer can maximize only his/her expected utility through buying or not buying the insurance (Varian, 1997). We now turn to the other important assumption regarding the consumer that we shall abide by – intelligence. The assumption of intelligence comes from nomenclature of game theory.

Game theory is essentially a method of mathematically modeling situations of conflict or co-operation (Gibbons, 1992). Intelligent players are players who have the capacity to infer anything about the game that we, the studiers of the game are. More precisely, the implication of the players being intelligent is that if we are able to infer that a given strategy is optimal for any particular player subject to the strategy choice of the rival players, then each and every player of the game will be able to draw the same inference as well (Kreps, 1990).

We shall assume that the consumer under consideration is both rational and intelligent. We model the given situation as that of a two player stage game. Player one is a rational and intelligent consumer and Player two is Mother Nature. To keep things simple we assume that there are two possible states of the world - accident and no accident; and which one is to be realized is a decision made by Mother Nature. Suppose Mother Nature chooses the no-accident state with probability P and this probability is common knowledge.

At the time of deciding on the purchase, Player 1 does not know whether he faces an accident or not. Suppose Player 1 earns X1 if the no accident state materializes and earns X2 if the accident state materializes, where X1> X2. Essentially we are assuming that the monetary value of the consumer’s health to himself if there are no accidents is X1 and this reduces to X2 if there is an accident. Define U(X) as the consumer’s utility function with U’ > 0 and U’’ < 0 => U (X1) > U (X2). Now, to bring in the role of insurance in this setup, suppose that the consumer can purchase insurance against the accident state.

Particularly, assume that if the consumer pays a premium ‘K’ then a lump sum transfer of ‘L’ is made to him if the accident state is realized in stage 2. Therefore, contemplating purchasing insurance can be rational only under the following condition: U (X2) < U (X2 +L-K). Mother Nature picks the state of the world. We assume her to be indifferent between the ‘