Payoff matrix

We give the payoff matrix of a game whose two players are X and Y... 

Decision Theory Formalism in the Behavioral Sciences.46—A formal method for examining decisions is developed through the use of a utility matrix [ tj] similar to the payoff matrix of game theory. In this matrix the rows correspond to the various possible acts of a decision-maker (e.g., to invest money in enterprises AltA2, -, Am) and the columns to various states, i.e., circumstances (e.g., possible levels of development of each enterprise) under which the acts are performed. The element y gives the utility (return or value) for using act At when state sf prevails. 

Table 9.1 Typical Payoff Matrix for Two-Member Teammate s Dilemma Problem...

Table 8.6 Market Share Payoff Matrix Market Share of Firm X...

Table 8.7 Profit Payoff Matrix (Millions of Dollars)...

Construct a profit payoff matrix between two firms making Delos (see Section 2.2.3). Firm X has a 30,000-liter reactor and firm Y a 50,000-liter reactor. Let the price be set at three different levels. Estimate the market shares, production levels, and profits of the two firms. Is there a dominant optimal strategy or a mixed optimal strategy ... 

Figure S.2 Payoff matrix for the occupation safety stage-game...

FIGURE 6.16.5 The payoff matrix for an encounter between two individuals. If both are cooperators, they receive a mutual reward. A cooperator who meets a cheater loses something to the cheater (sucker s payoff). A cheater who meets a cooperator is tempted to cheat. When two cheaters meet, nothing is gained and punishment may ensue. (From Turner, P.E., Am. ScL, 93,428, 2005. With permission.)... 

Table 1. Site licensed companies payoff matrix.

The prisoner s dilemma is a classic problem of conflict and cooperation [20,1]. In its simplest form each of two players has a choice of cooperating with the other or defecting. Depending on the two players decisions, each receives payoff according to a payoff matrix. When both players cooperate they are both rewarded at an equal, intermediate level (reward, R). When only one player defects, he receives the highest level of payoff (temptation, T), while the other player gets... 

Determining due care is only half of the story. It is also necessary to see whether both parties will freely choose this level of care. Game theory is a powerful tool for investigating actual behavior. It uses a payoff matrix which indicates the total care and accident cost borne by each party conditional on the level of care by both parties. The payoff matrix for the first example is shown in table 7.3. Each cell of the matrix is defined by the level of care taken by the two parties. For example the upper-right cell represents the situation where the railroad takes care but Party A does not. Inside the cell in parentheses are shown the costs to the railroad and then, after the comma, to Party A. Because these are costs, they are shown as negative amounts. For example, in the upper-right cell the railroad incurs its expected accident costs of ten plus five which is the cost of taking care, and Party A only bears its expected accident costs of ten. 

Table 7.3 Example I s Payoff Matrix With No Liability...

B if Party B did not take care. For example in the first and third lines of table 7.2, the railroad can recover its 50 units of accident costs that it incurs from Party B. Given that the probabilities of an accident are 0.16 and 0.10 respectively, the expected liability costs to Party B are eight in line one and five in line three. The resulting payoff matrix is shown in the lower part of table 7.5. The railroad, correctly, prefers not to take care because it prefers 0 to -6 and -10 to -13. Party B will correctly choose to take care because it prefers -9 to -16 and -6 to -10. 

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