Game theory, in this essay, means the study of strategies adopted by rational decision-makers of economic agents in specific situations, analyzing outcomes of mathematical models of conflict and cooperation (Myerson, 1991). Its basic elements include players, actions, information, strategies, payoffs, outcome and equilibrium, among which, players, strategies and payoffs are the most essential; actions and outcome are called as rules of the game (Rasmusen, 2000).
The objective of the model is to establish equilibrium with the use of rules of the games. Nash equilibrium, an important terminology in Game theory, is the situation when two or more players are involved in the game, and each player is supposed to know other players’ equilibrium strategies; players will get nothing just by changing their own strategy (Gibbons, 1992: p. 8).
Entry deterrence game, as a typical example in industrial economics, can be seen in the competitive markets in real society will be regarded as an object to be discussed In the subsection, firstly, entry deterrence game will be put into four classical types of game theories for analyzing and different strategies for the players in the games will be work out by using the given models; then the use of game theory in real entry deterrence will be slightly discussed. Model Analysis The first situation is the entry deterrence under the static games of complete information.
Suppose that there is already a monopolist company B as the incumbent in a specific industry; another company A as the entrant wants to enter this market. All the information in this market is open to A and B. B, in order to keep its profit, will try to prevent A from entering the market. There are two strategies for A to choose—to enter or to stay out; if entry occurs, there will be two choices for B—to collude or to fight. Suppose the entry costs are 10; duopoly profit—100 will be split evenly to A and B if B collude when A enters.
Table 1 illustrates the payoffs under the combination of different strategies. Table 1 Payoffs to: (A—entrant, B—incumbent) There are two Nash equilibrium— (enter, collude) and (stay out, fight). If A chooses to enter and gets no fight from B, it will get 40 payoffs (minus 10 enter costs), and B will get 50. But if B tries to prevent, they will both get no profit. Thus, the best strategy is for B to permit the entry of A. Similarly, if the prerequisite is B will permit A, the best choice for A is to enter. When A decides not to enter, fight or collusion means the same for B.
Only when the fight from B is sure to occur, it is best for A not to enter. That’s why (enter, collude) and (stay out, fight) can be identified as Nash equilibrium. However, in static games, the time order of the players has not been reflected, which requires to put the entry deterrence into the dynamic games of complete information. In the dynamic games, incumbent can adjust its strategy according to the performance of the entrant. Likewise, entrant can choose whether to enter or not based on the degree of incumbent’s interference.
Figure 1, an extensive form called game tree, demonstrates the strategies of incumbent and entrant in the dynamic games of complete information. Figure 1 Payoffs to: (A—entrant, B—incumbent) If A chooses not to enter the market, there will be no difference for B to fight or collude which can always get a total benefit of 300. But since the game begins after A has already entered, the equilibrium (stay out, fight) is Nash but not subgame perfect. Only when A decides to enter, B will have to select between fight and collude.
In this situation, the best response for B is to collude which is inevitable. In the entry deterrence, if B wants to keep its whole profit without fighting with A, it will have to use the strategy of credible threat before the entry of A. A practical method is to promise to C (a third party) that if A enters, B will definitely fight; otherwise, B will pay 100 to C. In that case, if B permit A’s entry, it will lose 50 (50 profit minus 100 wager); if B fight, it will get 0 which is better than collusion, while A will lose 10 in the fight.
If such threat works, B will be able to remain the monopoly profit without paying the 100 wager; otherwise, B will face the competition from A. Generally, the higher the wager is, the more credible the threat becomes. In the above two situations, the hypothesis is all the structures, rule of the game and payoffs are disclosed to all the players. In the following section, entry deterrence in static games of incomplete information will be analyzed. Suppose incumbent has two types: high costs and low costs.
Incumbent owns complete information, knowing its type selected; while entrant only has incomplete information, knowing that incumbent has two costs types but is unclear about what type has incumbent chosen. Table 2 shows the different strategies in different types for A and B. Table 2 Payoffs to: (A—entrant, B—incumbent) Suppose the probability of A knows B as a high costs competitor is x; the probability of low costs will be (1-x), x?(0,1). When A chooses to enter, its expected benefit will be u1= 40x+ (1-x) (-10) =50x-10; when A decides not to enter, its expected benefit u2=0x+ 0 (1-x) =0.
Therefore, for A, only when u1? u2 or 50x-10?0, that is when the probability of high costs is larger than 20%, A will choose to enter. Postulate that x? 20%, the Bayesian Nash equilibrium is: (enter, collude) in high cost or (enter, fight) in low cost. If x<20%, then the Bayesian Nash equilibrium will be (stay out, fight). The last situation of entry deterrence is dynamic games in incomplete information in which there will be perfect Bayesian Nash equilibrium. It is the combination of subgame perfect Nash equilibrium and Bayesian Nash equilibrium.
Differ from static games of incomplete information, in the games, entrant can only judge with its former experience for reference and has no idea about the incumbent’s costs type. Let incumbent B first set a price—P, which may itself include information about B’s cost function since the favourable prices are different in different cost functions. Assume at price P*, only company of low cost can make profit while firm of high cost cannot bear it. Then, the perfect Bayesian Nash equilibrium is— incumbent of low cost chooses P*, and company of high cost set a relatively high monopoly price.
If entrant finds out the choice of P* of incumbent, it can deduce it as a low cost player and it’s better for it not to enter; otherwise, entrant should enter since incumbent is of high cost who will not fight. The above four types may imply the players’ performance in practical situation when the competition between incumbent and entrant occurs. In real market, matters are not perfect. Incumbent will try to avoid competitors’ entry in order to monopolize the market, while the fact is entrants always attempt to enter.
The fight between them is unavoidable, which will arouse the incurrence of “price war”, property right protection, entry threat and so on. The result varies a lot when one thing is sure that incumbent will pay costs to obstruct entrant to enter. The key factor is whether it is worth to do. For entrant, to resist the pressure from the incumbent, it can optimize its strategies, such as adding new uses or function to its products or services. Conclusion In this essay, four types of non-cooperative game theory have been used to analyze entry deterrence, which result in different strategies for the players in the games to choose.
In the static games of complete information, two Nash equilibriums have been got; in dynamic games of complete information, the effect of the chosen strategy of the player who acts first on the latter act player has been taken into account, suggesting that the incumbent prevent entrant from entering by making credible promise to threat; in static games of incomplete information, each player can determine its favourable strategy according to the given probability of the other one’s strategy; in the last situation—dynamic games of incomplete information, players perform only by their former experience.
In the last part, situation in real society has been analyzed and some suggestions have been made. All in all, the use of game theory distributes widely in actual market and it is an art to perform it well.
Gibbons, R. (1992). A Primer in Game Theory. London: FT Prentice Hall. Myerson, R. B. (1991) Game Theory: Analysis of Conflict. Cambridge and London: Harvard University Press. Rasmusen, E. (2000). Games and Information: an Introduction to Game Theory. 3rd ed. Oxford: Basil Blackwell.