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Unformatted text preview: ch 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:  Who is involved?  The rules of the game (i.e. who moves when? what do they know? what moves are possible?),  The outcomes (i.e. what happens? (a physical outcome)),  The payoffs. 294 Defin nition: A game tree, , is a finite c , collection o nodes, ca of alled vertice connect by lines es, ted s, a at cted (i.e. the exists a set of arcs ere s called arcs, so as to form a figure tha is connec conn necting any one vertex to another and conta x r) ains no sim mple closed curves (i.e. there does not exist a set o arcs connecting a v e e of vertex to itse elf). We c further assert that a game tre has a dis can ee stinguished node or ro this is d oot; wher the game starts. No let's co re e ow, onsider som examples to illustra the me ate conc cepts of info ormation se and perf ets fect recall. 295 In thi case, Ch is handler knows whether Joey chos to bring his umbrella or not but se he do oesn't know whether it is raining or not raining. w ORMATION SETS N INFO Joey has one in y nformation s (Joey1) and one m set move or dec cision to ma (bring ake an um mbrella or not). n ndler has tw informat wo tion sets. If it is true th Joey ha his umbr f hat as rella then Chan 1 Chan ndler is at in nformation set Chandl . If Joey forgot his umbrella then ler y Chan ndler is at in nformation set Chandl 2. He als only has one move or decision ler so s n to ma (a or b) yet he do not know if it is rain ake ), oes ning or sun (i.e. he doesn't nny know which ver w rtex he is at in each inf t formation s set). Now, what does this game tree look like if Chand does n know if J s e dler not Joey has umbrella but he do...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
- Spring '10