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- An Introduction To Game Theory: The Basics And Key Concepts
- Applied Game Theory and Strategic Behavior: 1st Edition (e-Book) - Routledge
Now hopefully you would be convinced that game theory is cool ; it is indeed the most important theory in social sciences as well as natural sciences and engineering. But what is it? Rational decision making : Each rational individual makes the best decision by comparing costs and benefits of available choices. Availability is affected by the state of the economy e. Aggregate equilibrium : The economic state itself is eventually determined in equilibrium from aggregation of individual rational choices e.
Game Theory extends this idea of rational choice and aggregate equilibrium further to analyze everything in the world, with a more general framework that captures how people interacts each other. In Economics, Game Theory has become the most essential theory to consider market structure and complex business interactions in more realistic ways beyond the simple model of perfect competition. Thanks to Game Theory, now we economists can effectively analyze huge variety of complex economic interactions and business tactics—to name a few, union bargaining, cartels, corporate financial structure, advertizement, antitrust conducts, government regulations, herding behavior, bank run, systematic financial crisis—with closer attentions to differences and complexity of interactions among decision makers in reality—not just by mindlessly applying a textbook model.
Game Theory is the common language to describe these various issues as well as an analytical tool.
Further, Game Theory has been applied to wide areas of social sciences and even natural sciences and engineering. Sociologists theorize social phenomenons such as discrimination and social network with game theoretic models. Political scientists uncover unintended outcomes through Machiavellian behavior in voting, election campaigns and political coalition from game theory. Computer scientists and engineers rely on game theoretic models to design multi-agent systems such as wi-fi network and on-line auction. Transportation engineers also use similar game theoretic models on congestion and road pricing.
Biologists have been developed another rich arena for game theory on to discuss evolution of species, contagious spread of diseases, and competition, corporation and communication between animals. Linguists and philosophers , as well as economists, gather to this arena Evolutionary Game Theory as a common ground to discuss evolution of and languages and social norms. It is indeed my main research field and so I see a quite wide variety of researchers from these disciplines as well as mathematicians and engineers in academic conferences.
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Game Theory provides an integrated analytical framework to formulate such various situations in common unified formats and to decipher complicated interactions, from the viewpoint of rational decision making and aggregate equilibrium, so people from various disciplines can exchange ideas and work together with the common language. In Econ , we focus on the most essential core concepts in Game Theory and revisit them again and again through various applications , rather than covering many isolated concepts.
The Nash equilibrium concept neglects this sort of information, because it is insensitive to what happens off the path of play. The simplest of these is the backward-induction solution that applies to finite games of perfect information. Its rational was already used in the preceding paragraph. Specify that the player, who can move at each such node, chooses whichever action that leads to the successive terminal node with the highest payoff for him in case of a tie, make an arbitrary selection. Now specify that each player at those nodes, whose immediate successors are penultimate nodes, choose the action that maximizes her payoff over the feasible successors, given that the players at the penultimate nodes play as we have just specified.
Then roll back through the tree, specifying actions at each node not necessary for the given example anymore, but one gets the point. Once done, one will have specified a strategy for each player, and it is easy to check that these strategies form a Nash equilibrium. Thus, each finite game of perfect information has a pure-strategy Nash equilibrium.
An encyclopedia of philosophy articles written by professional philosophers.
Backward induction fails in games with imperfect information. Figure 12 : A game not solvable by backward induction. However, if one accepts the argument for backward induction, the following is also convincing. The only Nash equilibrium of this game is a mixed strategy with a payoff of 0 for both players as argued in Section 1a. More generally, an extensive form game can be analyzed into proper subgames , each of which satisfies the definition of extensive-form games in their own right. Games of imperfect information can thus be solved by replacing a proper subgame with one of its Nash equilibrium payoffs if necessary repeatedly , and performing backward induction on the reduced tree.
This equilibrium refinement technique is called subgame perfection. Repeated games are a special kind of dynamic game. At the end of each stage, however, the same structure repeats itself. As discussed in the previous section, it can be equivalently represented as an extensive game where player 2 does not know at which node he is. All that changed from the original game from figure 4 is the nomination of the players Row becomes 1 and Col becomes 2 and the strategies C and D. A repetition of this game is shown in figure Instead of the payoff matrices, at each of terminal nodes of the original static game, the same game starts again.
The payoffs accumulate over this repetition: while in the static game, the strategy profile D,D yields 1,1 , the strategy profile D,D , D,D in figure 14 yields 2,2. These payoffs are written at the terminal nodes of the last repetition game. If a repeated game ends after a finite number of stages, it is solved by subgame perfection. Starting with the final subgames, the Nash equilibrium in each is D,D. Because the payoffs are accumulative, the preference structure within each subgame does not change recall from Section 1a that only ordinal information is needed here. Thus for each subgame at any stage of the repetition, the Nash equilibrium will be D,D.
Therefore, for any number of finite repetitions of the game from figure 4, subgame perfection advises both players to always play D. All this changes dramatically, if the game is repeated indefinitely. The first thing that needs reinterpretation are the payoffs.
Any positive payoff, whether large or small, would be infinitely large if they just summed up over indefinitely many rounds. This would obliterate any interesting concept of an indefinitely repeated game. Fortunately, there is an intuitive solution: people tend to value present benefits higher than those in the distant future.
In other words, they discount the value of future consequences by the distance in time by which these consequences occur. The second thing that changes with indefinitely repeated game is that the solution concept of subgame perfection does not apply, because there is no final subgame at which the solution concept could start.photograph.dev3.develag.com/naciones-reconstruidas-poltica-cultural-e-imaginacin.php
An Introduction To Game Theory: The Basics And Key Concepts
Instead, the players may reason as follows. Player 1 may tell player 2 that she is well disposed towards him, relies on his honesty, and will trust him i. Once he proves to be untrustworthy, she will distrust him i. In the infinitely repeated game, player 2 has no incentive to abuse her trust if he believes her declaration.
If he did, he would make a momentary gain from playing D while his opponent plays C. This would be followed, however, by him forever forgoing the extra benefit from C,C in comparison to D,D. Unless player 2 has a very high discount rate, the values the present gain from cheating will be offset by the future losses from non-cooperating.
More generally, the folk theorem shows that in infinitely repeated games with low enough discounting of the future, any strategy that give each player more than the worst payoff the others can force him to take is sustainable as an equilibrium Fudenberg and Maskin It is noteworthy that for the folk theorem to apply, it is sufficient that players do not know when a repeated game ends, and have a positive belief that it may go on forever. It is more appropriate to speak of indefinitely repeated games, than of infinitely repeated ones, as the former does not conflict with the intuition that humans cannot interact infinitely many times.
From a philosophy of science perspectives, game theory has an interesting structure. Like many other theories, it employs highly abstract models, and it seeks to explain, to predict and to advice on phenomena of the real world by a theory that operates through these abstract models. Game theorists often focus on the development of the formal apparatus of the theory proper. Their interest lies in proposing alternative equilibrium concepts or proving existing results with fewer assumptions, not in representing and solving particular interactive situations.
What is needed instead is an interpretation of a real-world situation in terms of the formal elements provided by the theory proper, so that it can be represented by a game form.
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In many cases, this is where all the hard work lies: to construct a game form that captures the relevant aspects of a real social phenomenon. To acquire an interpretation, the game forms are complemented with an appropriate story Morgan or model narrative. As regularly exemplified in textbooks, this narrative may be purely illustrative: it provides in non-formal terms a plausible account of an interactive situation, whose salient features can be represented by the formal tools of game theory.
A chain store, also called player A, has branches in 20 towns, numbered from 1 to In each of these towns there is a potential competitor, a small businessman who might raise money at the local bank in order to establish a second shop of the same kind. The potential competitor at town k is called player k. This will happen first to player 1, then to player 2, etc. As soon as this time comes for player k, he must decide whether he wants to establish a second shop in his town or whether he wants to use his owned capital in a different way.
Applied Game Theory and Strategic Behavior: 1st Edition (e-Book) - Routledge
If he chooses the latter possibility, he stops being a potential competitor of player A. If a second shop is established in town k, then player A has to choose between two price policies for town k. The cooperative response yields higher profits in town k, both for player A and for player k, but the profits of player A in town k are even higher if player k does not establish a second shop.
Player k's profits in case of an aggressive response are such that it is better for him not to establish a second shop if player A responds in this way. Selten , The narrative creates a specific, if fictional, context that is congruent with the structure of dynamic form games. The players are clearly identifiable, and the strategies open to them are specified.
The story complements a game form of the following sort:. Game form and model narrative together constitute a model of a possible real-world situation. The model narrative fulfills two crucial functions in the model. If the game form is given first, it interprets this abstract mathematical object as a possible situation; if a real-world phenomenon is given first, it accounts for the phenomenon in such a way that it can be represented by a game form, which in turn can be solved by the theory proper.
The theory proper on the left hand side of Figure 16 specifies the concept of a game, it provides the mathematical elements that are needed for the construction of a game form, and it offers solution concepts for the thus constructed game forms.
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The game form left half of the central circle is constructed from elements of the theory proper. The model narrative the right half of the central circle provides an account of a real or hypothetical economic situation.