Problems in Game Theory
Game theory is an optimality model considering costs versus benefits as well as the existing interactions between game participants. Game theory looks at the coexisting relationships between model participants and then predicts their optimal decisions in the model that would result in the best outcome. In this paper, we will look at the required outcomes that would cause a problem to be categorized as zero sum game, win-win game, satisfying solution game, and cooperative/non-cooperative games.
Zero-sum game is a term used in game theory to refer to those situations or plays whereby a gain of one person or player must be matched by an equal loss of another person or player. It implies that the outcome balances between the two players (no player gains and no player loses). The number of players involved can be any with a minimum of two players. Examples in financial markets include options and futures because the benefits enjoyed by a seller or buyer from exercising either an option or a future benefit are equal to the losses suffered by the party on the same.
Penny-matching game is an example of a zero-sum game. The game consists of placing the pennies on a bench, and if they match, it is a win. The gains enjoyed by the winning player are matched with the losses suffered by the other player. The combined payoffs from either outcome in a zero-sum game are always zero since the gains of one party are matched by equal losses by the other party as can be seen from the example demonstrated below.
Perfect competition in economics is assumed by a zero-sum game where all parties involved have all the relevant information necessary for decision-making. The stock market, in general, is considered a zero-sum game; however, it is a misconception. The stock market is related to gambling historically, which is a zero-sum game (Gintis & Herbert, 2000).
Trade agreements between the countries where the agreement significantly contributes to the trade between the involved parties are referred to as win-win situations. On the contrary, when two states are involved in a conflict, no matter which state wins, both parties suffer losses. These are referred to as lose-lose situations or games. In a win-win, or non-zero-sum game, the outcome of a game or undertaking benefits both parties involved. According to game theory, the total of the win-win game is not zero as for the zero-sum game, but it could be two or more according to game theory. It can be explained by the fact that, unlike zero-sum game, the outcome could be a situation where both parties win an equal amount.
Consider a family negotiation as an example. A wife and a husband contend about the division of responsibilities, where the wife contends that the household chores and taking care of children are similar to being a full-time employee like her husband. If the husband refuses to help and agrees with the wife, the wife loses since, statistically, unlike her husband, she will be working more hours a day. To reach a win-win outcome, the couple must reach a compromise. However, it should be noted that if they do not manage to, the husband will enjoy the benefit of working fewer hours a day compared to his wife. On the contrary, if they compromise, and the husband agrees to help with some household chores, the couple will attain a win-win situation. In such a scenario, the husband benefits by having a less tired wife, who, in return, will be more devoted to the relationship and less resentful. The Nash equilibrium in economics is an example of a scenario where the parties act in the interest of the group at large creating a win-win scenario. Everyone wants to win and no one wants to lose. Thus, the basis of a win-win situation is finding a solution to the question How can the game be played such that at last long no one loses? Selfish players can never create a win-win scenario (Fernandez & Bierman, 1998).
According to game theory, a satisfying solution consists of analyzing all the available alternatives until the best or the most acceptable solution to a problem is arrived at. Simon (1956) introduced a more appropriate term for this game, satisficing which is a combination of the words satisfy and suffice. This term was used to describe how decision-makers behaved when an optimum solution was not easily determined. Simon notes that decision-makers could find an optimal solution by determining a solution for a more realistic world or a more simplified world (Rasmusen & Eric, 2006).
Here, decision-makers go for the solution or choice satisfying most needs rather than going for the optimal choice. Consider a scenario whereby there is a variety of pens in a container, and the pen that can best accomplish a specific job is at the bottom of the container. The other pens, of course, can do the job but not as perfectly as the one at the bottom. Thus, satisficing is all about using the first pen that can do the job rather than wasting time searching for that specific pen at the bottom of the container that can perfectly do the job.
In economics, satisficing means attaining or obtaining a certain level of a particular variable, some minimum at least, without considering the maximization of its value. This approach is applied in a case of a firm where profit is not treated as a goal by producers but as a constraint. Firms must attain a critical level of profit, and after that priority is attached to other goals being attained (Simon, 1956).
Cooperative/Non- Cooperative Games
When binding commitments can be formed between players, such a game is called a cooperative game. An example is where the law requires the players to keep their promises. However, when considering the non-cooperative game, whatever is possible in cooperative games is not possible here.
Symmetric/ Asymmetric Games
In symmetric games, the one who is playing the strategies does not determine the payoff, but rather the existence of other strategies is what determines the payoff in a game. In a symmetric game, changing player identities without changing the strategies does not affect the payoff. In asymmetric games, no identical strategies exist for both players.
In this game, there are many parties involved. It is a type of a problem where the players involved are infinite. The outcome is determined by the steps taken by each of the players.
Infinitely Long Games
These are problems whose alternatives are infinitely numerous. Any of the alternatives can bring the desired solution, but the players are not aware of the best strategy until implemented. The final solution is known after all the strategies are exhausted.