Abstract
In this chapter, we will try to investigate how parties may develop strategies and orient the dynamics of a conflict to obtain their goals. In order to do so, we will make use of the technical framework of Game Theory. Our purpose will be to not only understand how parties may interact in a conflictual situation but also identify the necessary conditions to render this interaction positive and cooperative.
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Notes
- 1.
- 2.
Notice, however, that the outcomes of the raffle are not influenced by the actions of the players; therefore, just like in the case of the transatlantic crossing, we do not actually need Game Theory to model the reasoning of the players in this game.
- 3.
Thus, a Nash Equilibrium for the rock-paper-scissors game is for both players a mixed strategy in which rock has probability 1/3, paper has probability 1/3, and scissors has probability 1/3 Consider a player A. Assuming that the sum of the probabilities that opponent B would choose any single strategy is
PB(rock) + PB(paper) + PB(scissors) = 1
The result can be obtained as the solution of a linear system of the following equations that define the expected value (EV ) of a player for every possible outcome.
EV[PA(rock)] = 0 × PB(rock) + (-1) × PB(paper) + 1 × PB(scissors)
EV[PA(paper)] = 1 × PB(rock) + 0 × PB(paper) + (-1) × PB(scissors)
EV[PA(scissors)] = (-1) × PB(rock) + 1 × PB(paper) + 0 × PB(scissors)
The same holds true for the other player.
- 4.
On several occasions, the American philosopher Robert Brandom has warned against the instrumentalist approach to rationality that is pursued by rational choice theorists and adopted, for instance, just in Game Theory (Brandom, 2011, pp. 35–36, 71; 2002, pp. 3–4). Obviously, part of what is for a human being to be rational is to be able to assess whether their actions and beliefs are correct. But what are the criteria of correctness? One might think that it is how things are in the world: thus, a belief is correct if it corresponds to a fact, an action is correct if it corresponds to a norm, and so on. On the instrumentalist approach, instead, the correctness of a performance or a belief is assessed with respect to its success: for example, if I have a goal, and by acting upon a belief I achieve it, then the belief is correct. And yet, there are any number of reasons why the action could have been successful and any number of reasons why things could have gone wrong. The contingent success of an intentional action can be no criterion for correctness. Besides, if we assume that an agent should have beliefs about everything that could possibly go wrong with their action in order to be sure that their success is not merely contingent, then which one exactly would be the content of the belief whose correctness is tested against such a criterium?
- 5.
Cooperative games are games in which players might form coalitions that would allow them to obtain better payoffs than if they acted individually. Cooperation is enforced by binding contracts that guarantee transferable utilities within the members of a coalition and that make it convenient for players to adopt mutually beneficial strategies. Cooperative Game Theory investigates how the best coalitions should be formed and how utilities should be shared within the members of these coalitions. Crucially, however, it does not explain how cooperation emerges out of the self-interest of non-cooperative players and presupposes the possibility of enforcing binding agreements among them. (See Ichiishi, 1983, 1993; Owen, 1995; Cruriel, 1997; Ichiishi & Yamazaki, 2006; Gilles, 2010.)
- 6.
The precise determination of the payoff matrix is obviously crucial for the results of the experiments. Had the ratio between the payoff for cooperation and defection been different, different strategies would have been more successful or less successful. The effects of a different payoff matrix would have been particularly relevant for the results of the evolutionary games (see the next section). This should not surprise us, however. To the contrary, it should confirm the intuition that the possibility of modifying the payoffs is what really determines the outcomes of a conflict in Game Theory.
- 7.
In Game Theory, the expectation of future interactions on the players’ part is represented in terms of a discount factor that applies to the payoffs of subsequent rounds of the game. For instance, if the discount factor δ is 0.5 and the payoff of a certain outcome for a certain player is 4 in a certain round, then the payoff of that outcome for that player in the next round should be 4 × 0.5 = 2. The idea is that the payoffs for future outcomes should be progressively diminished (the progression here is the progression of a geometrical series: e.g., 4 × δ + 4 × δ2 + 4 × δ3 ...) since they are less likely to be obtained. For instance, if the discount factor is 0, that means that player are sure that they will not get any payoff for future games. On the contrary, if the discount factor is 1, they are sure that they will play any future round and get their payoffs.
- 8.
Notice that this is a exceedingly strict condition rarely satisfied in real conflictual situations, where the parties have to give interpretations of each other’s strategies.
- 9.
- 10.
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Turbanti, G. (2022). Conflict Dynamics. In: Philosophy of Communication. Palgrave Philosophy Today. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-12463-1_10
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