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| same as a zero-sum game, where players' interests are in complete conflict. |
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| players face some limitation of information |
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| incomplete/asymmetric information |
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| one player knows more than another does |
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| strategy using signals wherein the player provides objective evidence or by actions that are credible proof of his information |
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| strategy taken by the less-informed party where the more-informed player will have to take some action that credibly reveals his information |
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| joint-action agreements are enforceable |
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| enforcement not possible and individual participants must be allowed to act in their own interests |
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| (all) choices available to the players |
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| a payoff calculated probabilistically |
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| players are perfect calculators and flawless followers of their best strategies |
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| each playing is using the strategy that is the best response to the strategies of the other players |
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| extensive form of a game, shows all he component parts of the game |
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| single action taken by a player at a node |
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| cutting branches when we are certain that an action in a sequential move game will not be chosen |
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| rollback / backward inducion |
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| looking ahead and reasoning back to determine behavior in sequential-move games |
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| when all players choose their optimal strategies found by doing rollback analysis |
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| comes from ability to commit oneself to an advantageous position and to force the other players to adapt to it |
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| comes from the flexibility to adapt oneself to others' choices |
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| basic initially specified actions |
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| list of strategies, one for each player, such that no player can get a better payoff by switching to some other strategy that no player can get a better payoff by switching to some other strategy that is available to her while all the other players adhere to the strategies specified for them in the list |
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| cell-by-cell inspection / enumeration |
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| check every cell to see if the strategies that generate it satisfy the definition of a nash equilibrium |
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| notion of what the others are choosing in simultaneous move games |
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| game in which two people might not cooperate even if it is in both their best interests to do so |
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| strategy chosen that is better than another strategy for one player, no matter how that player's opponents may play |
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| locating all possible nash equilibria of a game |
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| choose the strategy that minimizes the opponent's best response |
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| where it is important for both that the two people achieve one of the equilibria, but which one is immaterial because the two yield equal payoffs |
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| equilibrium more likely to be chosen by the players because it seems special, natural or relevant to them. |
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| games that require getting the preferred equilibrium outcome only if each has enough certainty or assurance that the other is choosing the appropriate action |
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| 2 player coordination game where two Nash equilibria occur where both agree on one outcome, but each prefers their own outcome |
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Definition
2 player simultaneous zero-sum game; A game where each player has two strategies, say Macho and Wimp,
such that [1] both (Macho, Wimp) and (Wimp, Macho) are Nash equilibria, [2] of the two, each prefers the outcome where he plays Macho and the other plays Wimp, and [3] the outcome
(Macho, Macho) is the worst for both. |
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| when players have a wide range of possibilities of strategies available |
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the part of a multimove game that begins at a particular node of the original game;
the game that begins at any node of the decision tree |
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| set of imperfect information for the player, as she can't distinguish between the nodes in the set given her available information |
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| only plan of action starting at a node is part of the full strategy pertaining to that subgame |
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| subgame-perfect equilibrium (SPE) |
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Definition
set of strategies, one per player, such that at every node of tree (whether or not the node lies along equilibrium) the continuation of the same strategy in the subgame is optimal for the player who moves there;
equilibrium found by applying rollback to the extensive form game/decision tree |
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Term
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Definition
1) simultaneous or sequential
2) pure conflict or alignment of interests
3) one time or iterated
4) limited and asymmetric information or not
5) fixed or manipulable rules
6) cooperative or non-cooperative |
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| simplest, as each player makes only one move |
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| criticisms of rollback theory |
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1) too simplistic to do justice to complex trees
2) rollback not really observed in simple games |
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| when successive (iterated) elimination of dominated strategies leads to a unique outcome |
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| focal point (convergence of expectations, requires common knowledge of choices and communication) |
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| best response of firm 2 to q1 |
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| competition is incredibly intense even though there are only 2 firms |
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| Nash Eq 3 conceptual merits |
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Definition
1) fits naturally with individual, non-coop games
2) fits with equilibrium concept
3) reasonable - other proposed solution would have worse problem |
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1) games can have many or no Nash Eq
2) ignores large risks from uncertainty |
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| Dominance in sequential move |
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| dominance important for later mover in sequential game |
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A game where each player chooses and implements his action
individually, without any joint-action agreements directly enforced by other players |
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| an interaction where both players are aware of the cross-effect of actions taken |
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| action situations where each person can choose without concern for reaction or response from others |
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| choices available to players (complete plan of action) |
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| single action taken by a player at a node |
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| a strategy is credible if its continuation at all nodes, on or off the equilibrium path, is optimal for the subgame that starts at that node |
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