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Game Strategies with Incomplete Information Case Solution

Most players in the market make their decision on the game strategy to choose in a competitive market. The decisions are always based on the market information, especially about the strategies chosen by their competitors. However, there are cases where the competition involves incomplete information and determining the decision by players may not be difficult. Therefore, Bayesian game entails several players in which an individual player has its belief on the payoff that involves the payoff of another player. This situation occurs when there is no perfect information in the market. Therefore, this discussion will focus on the dynamics of game strategies with incomplete information about the market.


The case of incomplete information in the game strategy involves a decision to enter or not to enter a market. If firms decide to enter, with a consideration that a competitive firm is already in the market, there is a probability that the two firms are going to have a change in the payoff. This incomplete information game strategy always applies to firms that are anticipating entering the market without knowing the strategy the other firm, which is a competitive firm is going to take. The tree below indicate the decision procedures involved in an attempt to reach Nash- Equilibrium

Game strategies with incomplete information

According to this tree, firm 1 is considering to enter a market. It has two decision to make, that is either to enter (E) or not to enter (N) and a firm 2 that is already in the market. In case of firm 1 does not enter the market, the payoff for it is 0 while firm 2 gets a payoff of 2.  On the other hand, in case firm 1 decides to enter the market, it payoff depend on the decision for firm 2. The incomplete information is whether firm 1 is strong or weak.  In the case of firm 1 is strong and firm to decide to fight, it means that both of them are going to lose with a payoff of (-1, -1). On the other hand, in firm 1 is weak and firm 2 decides to fight, firm 2 is going to get a payoff of 0 while firm 1 gets a payoff of -2. This will force firm one to exit the market due to the extent of losing it is likely to incur.

There exist two Nash equilibriums in this game that is, firm 1 decides not to enter and firm 2 decides to fight no whether the decision of firm one. The second Nash equilibrium is firm 1 enters the market in its weak vision and gets a weak vision of firm 2. In this case, there is going to be a payoff of (1, 1). It’s hard to determine the decision which will be taken by firm 2 when firm 1 enters and firm 2 does not also know the strength of firm 1. This brings the concept of incomplete information in the game strategy. The decision by a new firm to enter the market, therefore, has a lot of implication for both the incumbent firm and the entering firm. Therefore, it has a lot of implication to equity shareholders.

When making a decision to fund crown company equity shares, one has to take a keen analysis of the market and analyze the strength and weaknesses of that particular firm in which one intends to venture. The individual should also analyze the strengths and weaknesses of the competitor firm, which is already in the market. There is a need to take a comparison between the two firms and compare if there is a competitive advantage of the incumbent firm. Therefore the decision to venture into the market or to fund a new firm in the market will depend on the anticipated strategy that both firms are likely to take to exist in the market.

In this kind of game, the new entrant player 1 will choose a strategy to take. Based on the incomplete information, the incumbent player 2 will choose its own strategy to play without considering or knowing what player 1 has chosen. In a case where both the players choose the same strategy, it is referred to as pooling equilibrium.in case the strategies chosen are distinct; the game is referred to as separating equilibrium.  Taking a pooling equilibrium strategy by the new company will encourage the investors to put their finance in the business since they will be sure of sharing the market with the existing company. In this case, when both of them decide to fight based on their different strategies or both of the players choose not to fight and still share the same market. On the other hand, the choice of a separating equilibrium will scare away investors from the company and since it will result to the company being removed from the market by the incumbent Company

The game plan for incomplete information requires a keen analysis of the strengths and weaknesses of the competitor. In this case, a firm will choose a strategy that will make it better off than the other firm. The Nash equilibrium that is applied in this kind of game, either leads to one firm being satisfied with its action through very high payoffs while the other get nothing and decides not to enter the market with fear of getting a negative payoff. The second Nash equilibrium will entail sharing the market a between the new entrant and the incumbent player, a decision which leads to fairness to all the players. Therefore, it is the responsibility of the finances of the new entrant to have clear market knowledge on the strength of the incumbent player in the market. This action will make them know whether they will exist in the market or if they will be flashed out by the other player.


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