Posted by Alex M Thomas on July 3rd, 2007
Four persons A, B, C and D have to share Rs 4 among themselves in units of one rupee. First A proposes a distribution and all of them, including A vote on it. If at least 50% of those voting agree with A, the proposal is accepted. If not, A loses her voting rights and B gets to propose a distribution and all except A vote on it. Once again B’s proposal is accepted if at least 50% of those eligible to vote agree on it. If not, B also loses her voting rights and C gets to propose and so on to D. Assume that each person prefers more money to less and will always vote against a distribution in which she gets zero. What distribution would A propose?
This is a sequential game. It is one in which players make decisions (or select a strategy) following a certain predefined order, and in which at least some players can observe the moves of players who preceded them. If no players observe the moves of previous players, then the game is simultaneous. [Game Theory.net]
This is also one of perfect information. If every player observes the moves of every other player who has gone before her, the game is one of perfect information. [Game Theory.net]
In the sequential game with perfect information, A will propose 3 for himself and 1 to D. This will be accepted by both A and D. D will accept anything more than 0; the reason being that, if all the proposals are rejected and the 4 rupees come in Cs hand, he will take all 4 for himself and since he will will vote for himself, the proposal will get accepted.
In such a game, the one makes the move first will have undue advantage.
On Perfect Competition
This market environment is extensively studied in Economics and is considered as a “Perfect” environment especially on the basis of efficiency.
This write up explains the concept of perfect competition succinctly.
Is such an environment favourable for all ? Competitive markets emphasise the importance of having perfect information as a pre requisite for a competitive equilibrium; one which is also Pareto Efficient.
The consumption decisions taken are sequential in nature. The consumer decides to purchase the commodity or service keeping in mind the price; which has been fixed earlier keeping in mind the consumers preferences. The outcome will always favour the producer (In a perfectly competitive market) as he makes the decision of pricing first.
On Pareto Efficiency
An outcome of a game is Pareto efficient if there is no other outcome that makes every player at least as well off and at least one player strictly better off. That is, a Pareto Optimal outcome cannot be improved upon without hurting at least one player. [Game Theory.net]
If the objective in an economy is Pareto Efficiency, then it can be achieved by a competitive market. But, it does not take into consideration equity in distribution. For example, in the game mentioned above, an allocation which leaves A with all the 4 rupees is Pareto Efficient, because in order to make someone better off, A has to be made worse off.
In India, the objective is to reduce Poverty and make growth more wide spread rather than growth being segregated in nature.
The idea that we cannot achieve the ideal state of perfectly competitive market equilibrium might seem pessimistic. Some economists insist upon holding the capitalist system to a standard of competitive equilibrium. Failure to meet this standard constitutes a “market failure” that warrants government intervention.[MacKenzie 2006]
So, is a market environment with perfect information desirable?