76. GAME THEORY MODELS

OBJECTIVE

Anticipate competitors’ strategic decisions.

DESCRIPTION

Demand forecast or pricing models aim to find the optimal solution to maximize the benefits. However, this optimization usually does not take into consideration the fact that competitors are not static actors and will probably react to strategic decisions.

Game theory models take into account other players’ actions, and they offer theoretically an equilibrium in which no player can be better off from changing their strategy (Nash equilibrium). There are four main types of game theory models:

• -     Static games of complete information: movements are simultaneous and all the players know the payoff functions of the others;
• -     Dynamic games of complete information: movements are sequential and all the players know the payoff functions of the others;
• -    Static games of incomplete information: movements are simultaneous and at least one player does not have complete information about the payoff of the others;
• -    Dynamic games of incomplete information: movements are sequential and at least one player does not have complete information about the payoff of the others.

Another important element of game theory models is the repetition of the games , due to the fact that the strategy of players can change depending on the number of games. In this case we can calculate the net present value of future outcomes, since the nearest payoffs are more valuable than the most distant ones. There is also a series of assumptions when applying these models:

• -          Players are rational;
• -          Players are risk neutral;
• -          Each player acts according to his/her own interest;
• -      When making a decision, each player takes into consideration other players’ reactions.

Static (simultaneous) games are usually represented by payoff boxes, of which the most famous example is the prisoner dilemma. In this case the dominant strategy for both prisoners is to defect, since, in spite of the decision of the other prisoner, for both the decision to defect is the one with the higher payoff.

Prisoner’s Dilemma

On the other side, sequential games are usually represented by decision trees with the payoffs and decisions of the players.

Decision Tree with Players’ Payoff

Some common applications to business are:

• -          Market entry decision making
• -          Price modifications
• -          Quantity modifications

To find the solutions to these games, we use demand, supply, cost, and utility functions. Depending on the possible decisions that the players make, calculating these functions will define the payoff of players to determine the equilibrium of the game. When information is not known, we can use assumptions and weight them with a probability percentage, but this requires the creation of more complex models.

The template that I propose aims at profit maximization based on decisions about price changes. Profits (or payoffs) are calculated by the difference between a cost function and a demand function. The demand is a function of the price elasticity of the market and the cross-price elasticity with other competitors (this information can be gathered through several pricing techniques, for example choice-based conjoint analysis or brand–price trade-off).

More models are available online (Cournot, Bertrand, and Stackelberg games), and there are several Excel templates (for example http://econpapers.repec.org/software/uthexclio/). Data about competitors’ market share, costs, production limits, and so on should be estimated using industry data, published reports, and experts’ opinion (brainstorming, workshops, etc.). Prices can be collected more easily, since they are usually public. Data about price elasticity are calculated through surveys that include questions for price analysis techniques.

TEMPLATE

Download the Game Theory Models Template