SOME IMPORTANT EXAMPLES OF GAME THEORY

To Collude! or Not to Collude “Isthe noncooperative Nash equilibrium an efficient one that is in the best interests of the two players? One of the important l~ns of game theory is thin the noncooperative equilibrium can be inefficient for the players. Figure 11-5 highlights this point The starred Nash’ equilibrium in cell D brings in less total profit for the duopolists than any of the other outcomes. The best joint solution is A, with each duop- “olistcharging the high price and earning total profits of $300. The worst is the noncooperative Nash equilibrium with total profits of $20. ” How can the Nash equilibrium survive when both oligopolists together are earning less than they would with any other outcome? Remember Adam Smith’s maxim: “People of the same trade seldom meet t~ gether.. .. but the conversation ends … in some contrivance to raise prices.” Why don’t the firms just collude and choose the monopoly price? Let’s consider the cooperative equilibrium, which occurs when the players act in unison and set strategies that will maximize their joint payoffs. They may decide to form a cartel, setting a high price and dividing all profits equally between the “firms.Clearly, this will help the duopolists at the expense of the  consumers.

But it is not always so easy to “reach and sustain the cooperative monopoly solution. To begin with, cartels and collusion in restraint of trade are illegal in most market economies. But the highest hurdle is self-interest., Say that the price has been collusively set at (high, high) in cell A of Figure 11-5. Then Amazing “secretly decides to sella little output at a lower price, in effect moving to cell C. Amazing might be able to do this undetected for a while.

During this time, Amazing would earn higher profits, $150 instead of $100. Eventually, nEwBoob would notice that its profits had fallen. It would then reassess its strategy and, perhaps concluding that the cartel had come unglued, cut its price to the normal level. If the cooperative equilibrium (high, high) was not enforceable, the firms would quickly gravitate to the non cooperative or Nash equilibrium in outcome D (normal, normal). , We can apply this reasoning, to perfectly com markets as well. A pnftdIJ t::OfIIpelitiw t!f/IUIi~, riUflt is a Nash ur nonc:oopemtiw «JUilibriuflt in which .ch firm and consumer maka decisioras by talcing 1Mprices of everyone ~ as given. In this equilibrium, each firm maximizes profits and each consumer maximizes utility, leading to a zero-profit outcome in which price equals marginal cost. Recall Adam Smith’s doctrine of the’ invisible hand: “By pursuing [an individual’s] own interest, he frequently promotes that of society more effectually than when he really intends to promote it.” The paradox. of the invisible hand is that, even, though each person is behaving in a non cooperative manner, the economic outcome is socially efficient. Moreover, the competitive equilibrium is a Nash equilibrium in the sense that no individual would be better off by changing strategies as long as all other individuals continue with their strategies. In the perfectly competitive world, non cooperative behavior produces the socially desirable state of economic efficiency. , By contrast, if some’ parties (such as) were to ~and decide to move to the monopoly price in cell A, the efficiency of the economy would suffer. This suggests why governments want to enforce antitrust laws that contain harsh penalties for those who collude to fix prices or divide up the markets.

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