Lecture19 - Lecture #19 GAME THEORY THEORY NON-COOPERATIVE...

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Lecture #19 AME THEORY GAME THEORY NON-COOPERATIVE GAME THEORY here are two broad approaches to decision problem analysis using game theory The There are two broad approaches to decision problem analysis using game theory. The distinction lies between cooperative and non-cooperative games. This distinction does not mean that agents necessarily cooperate in cooperative game eory nor does it mean that agents necessarily do not cooperate in non- ooperative theory nor does it mean that agents necessarily do not cooperate in non cooperative game theory. What is the difference then? “Cooperative” means that the players can write binding contracts on their actions. For example, in cooperative game theory, players can commit to actions, which – when they have to be taken, possibly end up being against that players interests at that point in time. For instance, a player may commit to becoming a member of a coalition that is bound via contract to behave a certain way in a given state of the world…once that state of the world presents itself (if it ever does) the coalition is obligated to act as they said they would, even if there are better payoffs from another course of action.
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By contrast, non-cooperative game theory promises no such commitment to future actions. When a set of moves results in a player’s turn to decide upon a move going forward, the player is not constrained by any prior commitments and will decide their move based on their best personal outcome. We will only concern ourselves with non-cooperative game theory in this course. There are two distinct ways of representing non-cooperative games. EXTENSIVE FORM GAMES A game in extensive form provides us with a way of describing: [1] Who is involved? [2] The rules of the game (i.e. who moves when? what do they know? what moves re possible?) are possible?), [3] The outcomes (i.e. what happens? (a physical outcome)), ] The payoffs [4] The payoffs.
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Definition: A game tree, Λ , is a finite collection of nodes, called vertices, connected by lines, called arcs, so as to form a figure that is connected (i.e. there exists a set of arcs connecting any one vertex to another) and contains no simple closed curves (i.e. there does not exist a set of arcs connecting a vertex to itself). As per our definition, this diagram would not be a game tree. This is due to the fact at the figure is not I this a game tree? that the figure is not connected…the set of arcs does not connect any one vertex to another. s t s a ga e t ee Circle “YES” or “NO” s per our definition this diagram As per our definition, this diagram would not be a game tree. This is due to the fact that the figure, while connected, contains a simple closed curve (there does exist a set Is this a game tree? Circle “YES” or “NO” of arcs that connect some vertices to themselves).
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As per our definition, this diagram would be a game tree. This is due to e fact that the figure is connected the fact that the figure is connected and does not contain a simple closed curve (there does not exist a set of
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Lecture19 - Lecture #19 GAME THEORY THEORY NON-COOPERATIVE...

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