sequential equilibrium example

/S/GoTo 0000018244 00000 n /ColorSpace/DeviceRGB /Bounds[4.00005] /C0[0 0 0] /Resources 11 0 R For example, suppose we had two players, and player 1 was able to choose their action before player 2 could choose theirs. 0000041481 00000 n endstream We show that if the set of TMs that the agents can choose from is nite, then an . 0000008728 00000 n 0000009186 00000 n /ShadingType 2 endstream 2 In the case of an Enemy type, he enjoys seeing how player 2 unwraps a box with a frog inside! 19 0 obj Unfortunately, both perfect equilibrium and sequential equilibrium have been dened only in games of perfect re-call, where players remember all the moves that they have made and what they have observed. A Second Example Two Nash Equilibrium Only one of them is credible We need some formal way of capturing this idea of credibility. 0000039808 00000 n 0000040084 00000 n /FunctionType 2 /FunctionType 2 0000024898 00000 n 0000043928 00000 n sequential rationality (as SPNE, but applied to contexts of incomplete information). Answer: A subgame perfect equilibrium does not require sequential rationality, and weak sequential equilibria do not require subgame perfection off the equilibrium path. /Bounds[2.65407] >> Found inside Page 1143.4 Numerical Analysis In this section, we numerically analyze some examples to illustrate the behavior of the model. In this example the sequential equilibrium occurs at the intersection of the C-line and T-line. u.h 0000015581 00000 n /D(Navigation21) 0000036795 00000 n 0000026720 00000 n 0000053138 00000 n /BBox[0 0 362.835 2.654] /Filter/FlateDecode Solving sequential games with backward induction. Loosely, a sequential equilibrium is a Nash Equilibrium that /Border[0 0 0] /Type/XObject Example of sequential equilibrium Consider the following game 1 2 3 a b 0,0,0 3,2,2 0,0,1 4,4,0 1,1,1 1 1 1 1 Each player has two actions (left and right). 0000041188 00000 n 0000046242 00000 n /N 1 0000037547 00000 n 0000014576 00000 n For example, suppose we had two players, and player 1 was able to choose their action before player 2 could choose theirs. 0000044221 00000 n 0000026367 00000 n 0000034094 00000 n For example, let's examine the decision a company faces when trying to break a market which is currently a monopoly. This book brings together the joint work of Drew Fudenberg and David Levine (through 2008) on the closely connected topics of repeated games and reputation effects, along with related papers on more general issues in game theory and dynamic 0000065233 00000 n 5. %%EOF Found inside Page 228Non-existence of equilibrium with RPb I 1, RPS I 0, 6b I 0.8, 65 I 0.8, (Tb I {5,8, 9},P,? I {0.5,0.3,0.2}), T, I 10, In this section we produce an example of bargaining that does not admit any pure strategy sequential equilibrium. 0000047445 00000 n 0000024080 00000 n Preliminary Concepts Sequential Equilibrium Signaling Game Application: The Spence Model Application: Cheap Talk Weak sequential equilibrium: example (cont.) 0000046989 00000 n 2 Preliminaries In this section, we discuss a number of issues that will be relevant to our de nition of sequential equilibrium: imperfect recall and absentmindedness, what players . u.h In extensive-form games, we can have a Nash equilibrium prole of strategies where player 2's strategy is a best response to player 1's strategy, but where she will not want to carry out her plan at some nodes of the game tree. This is a textbook for university juniors, seniors, and graduate students majoring in economics, applied mathematics, and related fields. 0000025731 00000 n ante sequential equilibrium. Lets show this with an example. 0000015968 00000 n 0000031425 00000 n /FunctionType 2 Subgame Perfect Equilibrium Examples Example: Chain-Store game Suppose that the chain store plays the chain-store game sequentially with K potential competitors in K di erent cities. >><< 0000050081 00000 n Found inside Page 323In contrast , sequential equilibrium is defined for general games and does rule out the equilibrium ( L , A ) in figure 8.1 PBE to multi - stage games , and applies it to a repeated version of the public - good game of example 6.1 . 135 0 obj<>stream There are other restrictions imposed by the notion of sequential equilibrium. 27 0 obj 0000019223 00000 n Sequential Move Games As stated before, sequential move games are simply where the order of movement matters. /D(Navigation2) 0000082694 00000 n /Subtype/Link /C0[0.2 0.2 0.7] 0000015058 00000 n 0000025033 00000 n Microeconomic Theory is based on lecture notes for a graduate course in microeconomic theory. It covers a broad range of topics, and to some extent the lecture structure is retained in the style of the book. The first textbook to explain the principles of epistemic game theory. The theory and applications covered in the first part of the book fall under the so-called 'classical' approach to game theory, which is founded on the paradigm of players' unlimited rationality. /Filter/FlateDecode /Domain[0 1] perfect Bayesian Nash equilibrium in which player 1 orders quiche independent of this type, and player 2 ghts when he observes a beer. %PDF-1.4 0000043251 00000 n 0000027200 00000 n /N 1 0000009092 00000 n 0000009562 00000 n 0000039946 00000 n 0000027404 00000 n 0000044936 00000 n /Shading<< << 0000029565 00000 n >> /N 1 Sequential Move Games Road Map: Rules that game trees must satisfy. 0000043389 00000 n % 0000023193 00000 n In a separating equilibrium all types choose distinct actions, i.e. The two solution concepts are equiva lent in the games considered here. 0000019666 00000 n 0000052348 00000 n Electronic edition ISBN 978-1-61444-115-1 So when using mixed strategies the game above that was said to have no Nash equilibrium will actually have one. 0000038533 00000 n Sequential Equilibrium I An assessment (s; ) is asequential equilibriumof a nite extensive-form game with perfect recall if it issequentially rationalandconsistent. /Subtype/Link /A<< /Function<< The issue in both of the following examples is othe equilibrium path beliefs, namely I assigning positive probability to E playing a strictly dominated strategy othe equilibrium path. /Domain[0 8.00009] << 0000031203 00000 n /Type/XObject 0000033341 00000 n 0000048851 00000 n 0000053572 00000 n 0000046700 00000 n /Coords[0 0 0 18.57857] 0000012341 00000 n borrowing in which Ponzi schemes of limited scale are feasible. 0000036016 00000 n /FormType 1 /FunctionType 3 0000027052 00000 n /N 1 For instance in the above example there are two Nash equilibria: (NH,H) and (NL,H). Repeated games are an example of sequential games. /Function<< 0000041116 00000 n /Subtype/Link /Function<< /Functions[<< 0000060547 00000 n /A<< >> For example, in the topmost branch (all vote yes) each has a payoff of p . This paper offers an introduction to game theory for applied economists. >><< Did you know? 0000033671 00000 n Now you are familiar with some of the key concepts of Game Theory, the next step is to learn how to solve each game. 0000017182 00000 n >> 0000059821 00000 n 0000048549 00000 n /FunctionType 2 0000028732 00000 n /C0[0.5 0.5 0.5] /Encode[0 1 0 1] 0000039401 00000 n equilibrium, we thus say that SPNE is a renement of Nash equilibrium . Let also (k 1, k 2, k 3), be the sequence that . 0000024162 00000 n /Subtype/Form 0000020820 00000 n 0000017481 00000 n /C[0.5 0.5 0.5] For . trailer << /Size 1415 /Info 1301 0 R /Root 1304 0 R /Prev 548964 /ID[<0a34f7fde896f81c872a67188ecea7c2>] >> startxref 0 %%EOF 1304 0 obj << /Type /Catalog /Pages 1298 0 R /Metadata 1302 0 R >> endobj 1413 0 obj << /S 13337 /Filter /FlateDecode /Length 1414 0 R >> stream /Encode[0 1 0 1] 0000028819 00000 n Importantly, the later players must have some information of the first's choice, otherwise the difference in time would have no strategic effect. /Subtype/Form Similarly, in Example 3, any totally mixed sequence must generate the consistent belief (0,1) for the strategy prole under consideration (do this for-mally). 0000041905 00000 n 0000058706 00000 n [bkLoi3{;vkW=vS=w;'+73;R@)khji. /Resources 7 0 R >> Asking for sequential rationality in sequential-move games with incomplete information." /ProcSet[/PDF/Text/ImageC/ImageB/ImageI] 0000021313 00000 n
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