Approach to othismos through game theory

Dołączył: 09 Mar 2024 Posty: 1

Game theory is a mathematical analysis tool that allows us to shed light on any social situation of strategic conflict between rational agents who pursue well-defined objectives, applying it to the study of business competition in economics as well as to politics and the study of conflicts. international. Since it would be impossible to explain the mathematical details of the theory in this short essay, I will limit myself to basic intuitions in this specific war context. Those who wish to delve deeper into the topic have high-quality introductory texts available, such as Gibbons. Each army must, therefore, choose a single one of its four possible strategies without knowing the strategy that the opponent is deciding at the same time.

The first element in the description of a game is to determine the rational players faced . In our case there would be two: army A and B (or, if you prefer, the strategists of both). Then we specify the set of strategies available for each army, both having similar characteristics and with similar a priori probabilities of winning or losing BTC Users Number Data the battle (both have voluntarily accepted the risk of combat): both armies face each other with two wings (left and right) and can initiate an othismos (which we denote as “1”) or not initiate it (“0”) with each of them independently. Action “0” consists of fighting in somewhat more open lines in which individual effectiveness is greater and recoil is possible. Thus, each army has four strategies available , depending on whether it chooses “1” or “0” with each of its wings. We can therefore represent the set of possible strategies of each army as the following four ordered pairs: where the first component of Each pair represents the action of performing or not performing an othismos with the left wing and the second component represents the same options for the right wing.

We now move on to explain the consequences of each combination of strategies (or possible outcome of the battle). Each wing of an army faces the opposing wing of the other and will suffer a certain number of casualties depending on both strategies. If one wing of an army does not make othismos and neither does its opponent wing, each sufferscasualties, while if the wing without othismos faces the othismos of its opponent wing, it suffers no casualties because it retreats and causes a number of casualties to his opponent. On the other hand, two opposing wings in othismos also do not cause significant casualties. Furthermore, if one of the wings of an army (let's say it's A) does not do othismos and the other does, while the other two opposing wings do the same action (either "1" or "0"), then Army A will be outflanked and panic with uncontrolled retreat. In that situation, army A as a whole will suffeadditional casualties to those it already had in each of its wings. We know from the sources that this is the situation where the most casualties occur , so we assume that . Those are all the parameters we need to describe the strategic situation of our game.

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