Dominant Strategy
A dominant strategy in economics refers to a choice that yields the highest payoff for a player regardless of the choices made by other players. It is a strategy that is always the best option, regardless of the actions of other players. In game theory, identifying dominant strategies helps to predict the most rational choices for players in strategic interactions.
6 Key excerpts on "Dominant Strategy"
eBook - ePubGame Theory in the Social Sciences
A Reader-friendly Guide
- Luca Lambertini(Author)
- 2011(Publication Date)
- Routledge(Publisher)
...If this sort of automatic pilot does work, the resulting best reply qualifies as that player's Dominant Strategy. The rigorous definition is as follows. D EFINITION 3.2 Strategy i ∈ S i is (at least weakly) dominant for player i if it maximizes his/her payoff π i (i, s − i) irrespective of the opponents’ behaviour s − i, that is, if and only if If the above inequality holds strictly, then i is strictly dominant ; otherwise, if it holds as an equality for at least some admissible s − i, then it is weakly dominant. In agreement with Definition 3.2, if all players do have a Dominant Strategy (or at least one that is weakly so) and adopt it, the outcome identified by the combination of (at least weakly) dominant strategies will qualify as an equilibrium in dominant strategies, as follows. D EFINITION 3.3 Given a game G ≡ N, S i,π i (s), the outcome ≡. (1, 2,..., N), with i ∈ S i for all i ∈ N, is an equilibrium in (at least weakly) dominant strategies if and only if This concept deserves a few comments. In particular, it is worth dwelling upon the difference between the condition that must be satisfied for an outcome to be a Nash equilibrium and the one contained in Definitions 3.2 and 3.3 in order for a Dominant Strategy equilibrium to arise. While the former requires a player to identify the best reply to every possible strategy chosen by any rival – whereby no ex post regrets may exist – the latter poses a much stronger requirement, which consists in finding a strategy yielding a payoff systematically at least as high as that for any other strategies the same player could adopt, no matter what the opponents do. Relatedly, as we shall see below, the existence of an at least weakly Dominant Strategy for a player does not necessarily entail that this player's best reply will be unique...
eBook - ePub- Rob Dransfield(Author)
- 2013(Publication Date)
- Routledge(Publisher)
...A game occurs where there are two or more interacting decision takers (players) and each decision or combination of decisions involves a particular outcome (pay-off). The fate (or pay-off) of a player in a game depends not only on the strategies employed by the player but also on the strategy of other players.Much of the analysis that has been carried out by economists focuses on the benefits/ drawbacks of the players collaborating or competing with each other. Important ground-breaking work in game theory was carried out by the US economist John Nash. Nash developed the concept of the Nash equilibrium – a situation in which each of the players in the game arrives at an optimal solution given the potential response of a rival player.Case Study A competitive duopolyLet us consider an example of pure conflict in an oligopoly market by looking at a situation of a duopoly (i.e. a market containing two firms). We can call these two firms Shell and BP. Each firm controls half of the market. The illustration below shows that both firms have a wide range of possible strategies that they can employ to try to increase their market share. Each firm will hope that its strategy will increase consumer preference for its particular brand.As with a game of chess, the moves of each player will affect the other’s situation. Between them they satisfy the total market for petrol. Any increase in the market share of one will result in a reduction of the market share of the other. The total market is a constant sum. The game the two firms play is thus called a constant sum game.Let us now assume that Shell and BP have narrowed down the effective strategies that they can employ to increase market share. Shell is considering four possible strategies to gain the largest possible market share...
eBook - ePub- Bonnie Nguyen, Andrew Wait(Authors)
- 2015(Publication Date)
- Routledge(Publisher)
...CHAPTER 3 Key strategic tools DOI: 10.4324/9781315690339-3 3.1 Introduction As we have previously discussed, economic agents try to do the best they can for themselves; in other words, they try to maximize their objectives subject to the constraints that they face. Sometimes, it is sufficient to consider a consumer or firm’s maximization problem in isolation. But at other times, the strategic interaction between parties is important. In these situations, the individual’s choice of action will typically depend on what other parties choose to do. In this chapter, we outline a few basic tools that are useful in analysing these situations. We will later look at applications of these tools in Chapters 5 and 15. 3.2 The essentials of game theory Strategic interactions between economic agents can be analysed using game theory. This requires the relevant strategic interactions to be represented in the form of a game. For most people, the word ‘game’ brings to mind card- and board-games or sports. However, in economics, the term has a specific meaning. In particular, a game has the following elements: Two (or more) players. A complete description of what actions each player may take. A specification of each player’s payoff associated with the actions taken. For now, we will assume that each participant in the game has full knowledge of these things. That is, each player knows who the other players are, what actions each player may take, and the payoffs that each player receives if certain actions are taken. Note that this does not imply that each player knows what actions are actually taken by the other players. As you can see, the economic notion of a game is different but related to the everyday understanding of what a game is. In fact, the economic definition of a game would probably include most card- and board-games and sports, but also embraces a wider variety of situations. Consider the following examples. Example...
eBook - ePub- J. McMillan(Author)
- 2013(Publication Date)
- Taylor & Francis(Publisher)
...2. Basic Concepts of Game Theory DOI: 10.4324/9781315014562-3 This section introduces some of the more important ideas of game theory. No attempt is made at completeness; only those ideas which seem to be the most relevant to economics are discussed. 2.1 Definitions The distinctive feature of a game is the presence of interdependencies among the agents: one agent’s utility depends not only on his own actions, but also on the actions of each of the other agents. It is the agents’ awareness of interactions among their decisions which give rise to the subtle problems of game theory. (To take an example from elementary-textbook economics, the decisions of a monopolist are not game theoretic; the decisions of an oligopolist are game theoretic.) A strategy is a complete description of the agent’s planned actions. (In the case of the textbook oligopolist, a strategy is simply a level of output; and the set of strategies consists of all non-negative output levels.) Formally, a game (or, more accurately, a game in strategic form) consists of: a set of agents; a set of strategies for each agent, from which the agent chooses a particular strategy to play; and a utility function for each agent. Suppose there are n agents. Each agent, i, chooses a strategy a i from the set A i of possible strategies. Because it is a game, each agent’s utility, u i, depends on every agents’ strategy: u i = u i (a 1, …, a n), i = 1, …, n. An agent uses a mixed strategy if he deliberately randomizes his choice of strategy. If, on the other hand, the agent decides nonstochastically, he is said to use a pure strategy. Mixed strategies are used when agents have some incentive to conceal what they are going to do. In a zero-sum game, the sum of all agents’ utilities is always zero. A zero-sum game is a game of pure conflict: what one agent wins, some other agents must lose. Clearly a constant-sum game is equivalent, with appropriate normalization, to a zero-sum game...
eBook - ePub- Walter Schaeken, Gino De Vooght, Andr' Vandierendonck, G'ry d'Ydewalle, Gery d'Ydewalle, Walter Schaeken, Gino De Vooght, Andr' Vandierendonck, G'ry d'Ydewalle, Gery d'Ydewalle(Authors)
- 1999(Publication Date)
- Routledge(Publisher)
...Formally, an action is dominated when there is at least one other action that always yields a higher payoff for a player, no matter what the other player does. A game is solved by dominance when participants, by deleting dominated actions, are left with only one action. The individual actions surviving the elimination process constitute the solution of the game. In the preceding case, one can see that for Giovanna action A yields a higher payoff than B, whatever action is chosen by Paolo (6 vs. 5 and 4 vs. 2). Conversely, for Paolo, action B will yield a higher payoff whatever action is chosen by Giovanna (3 vs. 1 and 7 vs. 4). Thus, (A, B) is the solution of the game by dominance. The normative standing of dominance follows from the definition of preference (Kreps, 1990). This is why dominance appears to be an obvious principle to game theorists. However, the lesson of the psychology of reasoning is that we are not always good at seeing what seems obvious to experts (see Garnham & Oakhill, 1994). Thus, it is tempting to look at violations of dominance as good candidates for the understanding of naive deductive thinking in games. The concept of dominance is the weakest, and thus the most general, concept of rationality used in game theory. It implies only that one will avoid actions that are always less desirable than other ones available. Despite its appealing simplicity, the concept of dominance is not so easy to grasp as game theorists claim. A game matrix is a quite complex representation, within which dominance can be seen only if players adopt the right strategy. In order to see easily dominance relations, each player has to focus initially on the other’s actions to infer the ordering of consequences for him or her. In order to understand the logic of such a reasoning strategy, let us assume (for the sake of expositional simplicity) that participants represent the matrix as a set of conditionals...
eBook - ePub- Peter C. Ordeshook(Author)
- 2020(Publication Date)
- Routledge(Publisher)
...Generally, we will want to eliminate even weakly dominated strategies, and indeed, doing so often eliminates Nash equilibria which are unreasonable predictions. For example, if all persons have the same preference over some set of alternatives, it is nevertheless the case that everybody voting for their last choice is, under majority rule, a Nash equilibrium—no one has any incentive to shift unilaterally to some other strategy since doing so cannot change the outcome. Voting for one’s last choice, however, is weakly dominated, and, thus, such equilibria are eliminated if weakly dominated strategies are eliminated. For example, in a simple one-vote agenda, voting for one’s preferred alternative dominates a contrary vote. If one’s vote is not decisive, then it does not matter what choiceis made; but in the event that one’s vote is decisive, then it is always best to vote for the preferred alternative (assuming, as before, that one’s vote does not count negatively). With respect now to election models, it is fortunately the case that the sort of election scenarios that Figure 3.4b illustrates, spatial elections, have strategies that dominate others. For example, if candidates are concerned solely with whether or not they win the election, then for two-candidate elections, platforms located far from all ideal points are dominated by ones that are closer to those points. And since it seems unreasonable to suppose that anyone would choose a dominated strategy, it similarly seems unreasonable to suppose that a candidate, regardless of the election campaign’s dynamics, would choose such a strategy either...
