# A contribution to understanding game theory

Theory of games is a mathematical theory of participants deciding in a competitive environment, through which the analysis of social phenomena can be carried out. This theory is one of the ways in which to interpret or anticipate behavior and decisions in conflict situations, that is, in situations where the final solution of a problem does not depend solely on the decision of one participant, but also on the views of the other participants.

Such situations are most often characterized by a status in which participants have completely opposite views, and each of them seeks to derive maximum benefit from it. Since it is unpredictable and the environment within which there is a problem, in order to solve it, pure mathematical knowledge is not sufficient, but requires a multidisciplinary approach, which includes other sciences, such as economics, psychology, sociology. The relevance of economics to game theory is best demonstrated by the fact that Thomas Schelling and Robert Aumann received the Nobel Prize in 2005 for their contribution to understanding conflict and cooperation through the theory of games.

Basic elements of this theory are players, actions or moves, then the benefits that are achieved by choosing certain strategies and at the end of the set of information that the players have. The designated elements are rules of the game.

Players will insist on maximizing their own benefits and at the same time tailor a strategy that will draw the next move based on available information. All players are aware that the outcome of their action is not affected only by those, but also the actions of other players. The outcome of the game is the result, which is the product of all the mentioned variables. After each player chooses his strategy, a combination of strategies is obtained and it is called a balance.

Functioning of this theory can be mathematically set up and proved, but it can also be illustrated through a multitude of examples. One of these is the budget dilemma, which can help in getting the answer to the question of why governments in which there are more parties spend more than governments with fewer parties. (1) The assumption is that the two parties form the ruling coalition have reached an agreement on a fiscal policy that predicts spending is shared in accordance with electoral power.

Each party has two options, it can respect the agreement, or not, seeking to increase spending for itself, which ultimately can lead to an increase in the level of spending above the one agreed. If one of the parties decides to honor the agreement, the other accepts it in principle, and then immediately before the adoption of the budget changes the position for those budget items that only use their electorate, then the first party in the case of non-acceptance faces the collapse of the coalition and the early elections. Of course, each of these parties is also a veto player, which means that it can withdraw their ministers from the work of the government and thus cause a standstill in the work, or its fall.

In order to avoid the collapse of the coalition, the first party may also withdraw from a fiscal agreement, seeking a reciprocal increase in public spending in those areas it presumes to use to its electorate. If an agreement is reached, the coalition survives and a balance is established, which implies a total increase in public spending.

Of course, any similarity to the Bosnian-Herzegovinian reality is completely accidental. If it exists, John von Neumann and Oscar Morgenstern can be blamed for this. In the mid-20th century, they developed the basic principles of game theory as a mathematical and economic discipline that modeled the situation of the competition and the cooperation of various individuals and shaped it in the work of “Theory of Games and Economic Behavior”.

1. This example is “borrowed” from the book Pavlović, D. Teorija igara – Osnovne igre i primjena, FPS University in Belgrade, Belgrade, 2015, p.111-114