Strong Forward Induction

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Bingyong Zheng
Keyword(s):  
Solution Concept ◽  
Forward Induction ◽  
Equilibrium Outcome ◽  
Dominance Condition ◽  
Local Dominance

AbstractForward induction, as defined by Govindan and Wilson (2009. “On Forward Induction.” Econometrica 77:1–28), places a local dominance condition on off-equilibrium beliefs that restricts relevant strategy profiles for an equilibrium outcome to be infinitely more likely than profiles that include irrelevant strategies. Meanwhile, it places no global dominance restrictions and thus leaves open the possibility that a dominated strategy is deemed more likely than strategies dominating it. This paper defines strong forward induction, which improves upon forward induction. We also develop a solution concept called strong forward induction equilibrium that is obtained from iterative application of the strong forward induction criterion.

Self-enforcing Agreements and Forward Induction Reasoning

2020 ◽  
Author(s):  
Emiliano Catonini
Keyword(s):  
Dynamic Games ◽  
Subgame Perfect Equilibrium ◽  
The Self ◽  
Perfect Equilibrium ◽  
Forward Induction ◽  
Equilibrium Outcome ◽  
Equilibrium Refinements ◽  
Binding Agreement

Abstract In dynamic games, players may observe a deviation from a pre-play, possibly incomplete, non-binding agreement before the game is over. The attempt to rationalize the deviation may lead players to revise their beliefs about the deviator’s behaviour in the continuation of the game. This instance of forward induction reasoning is based on interactive beliefs about not just rationality, but also the compliance with the agreement itself. I study the effects of such rationalization on the self-enforceability of the agreement. Accordingly, outcomes of the game are deemed implementable by some agreement or not. Conclusions depart substantially from what the traditional equilibrium refinements suggest. A non-subgame perfect equilibrium outcome may be induced by a self-enforcing agreement, while a subgame perfect equilibrium outcome may not. The incompleteness of the agreement can be crucial to implement an outcome.

scholarly journals The implications of finite‐order reasoning

2021 ◽  
Vol 16 (4) ◽  
pp. 1605-1654
Author(s):  
Adam Brandenburger ◽  
Alexander Danieli ◽  
Amanda Friedenberg
Keyword(s):  
Experimental Data ◽  
Finite Order ◽  
Prisoner’S Dilemma ◽  
Solution Concept ◽  
Response Sequence ◽  
Forward Induction ◽  
Extensive Form ◽  
Strong Belief ◽  
Response Sets ◽  
Best Response

The epistemic conditions of rationality and mth‐order strong belief of rationality (R mSBR; Battigalli and Siniscalchi, 2002) formalize the idea that players engage in contextualized forward‐induction reasoning. This paper characterizes the behavior consistent with R mSBR across all type structures. In particular, in a class of generic games, R( m − 1)SBR is characterized by a new solution concept we call an m‐best response sequence ( m‐BRS). Such sequences are an iterative version of extensive‐form best response sets (Battigalli and Friedenberg, 2012). The strategies that survive m rounds of extensive‐form rationalizability are consistent with an m‐BRS, but there are m‐BRS's that are disjoint from the former set. As such, there is behavior that is consistent with R( m − 1)SBR but inconsistent with m rounds of extensive‐form rationalizability. We use our characterization to draw implications for the interpretation of experimental data. Specifically, we show that the implications are nontrivial in the three‐repeated Prisoner's Dilemma and Centipede games.

scholarly journals Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information

2013 ◽  
Vol 13 (1) ◽  
pp. 79-130 ◽  
Author(s):  
Pierpaolo Battigalli ◽  
Andrea Prestipino
Keyword(s):  
Asymmetric Information ◽  
Solution Concept ◽  
Solution Procedure ◽  
Common Belief ◽  
Forward Induction ◽  
Interactive Epistemology ◽  
First Order ◽  
Special Cases ◽  
States Of Nature

Abstract: We analyze forward-induction reasoning in games with asymmetric information assuming some commonly understood restrictions on beliefs. Specifically, we assume that some given restrictions Δ on players’ initial or conditional first-order beliefs are transparent, that is, not only do the restrictions Δ hold but there is also common belief in Δ at every node. Most applied models of asymmetric information are covered as special cases whereby Δ pins down the probabilities initially assigned to states of nature. But the abstract analysis also allows for transparent restrictions on beliefs about behavior, e.g. independence restrictions or restrictions induced by the context behind the game. Our contribution is twofold. First, we use dynamic interactive epistemology to formalize assumptions that capture foward-induction reasoning given the transparency of Δ, and show that the behavioral implications of these assumptions are characterized by the Δ-rationalizability solution procedure of Battigalli (1999, 2003). Second, we study the differences and similarities between this solution concept and a simpler solution procedure put forward by Battigalli and Siniscalchi (2003). We show that the two procedures are equivalent if Δ is “closed under compositions” a property that holds in all the applications considered by Battigalli and Siniscalchi (2003). We also show that when Δ is not closed under compositions, the simpler solution procedure of Battigalli and Siniscalchi (2003) may fail to characterize the behavioral implications of forward-induction reasoning.

scholarly journals Conditional Entropy: A Potential Digital Marker for Stress

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 286
Author(s):  
Soheil Keshmiri
Keyword(s):  
Resting State ◽  
Nearest Neighbor ◽  
Brain Activity ◽  
Solution Concept ◽  
Conditional Entropy ◽  
K Nearest Neighbor ◽  
Brain Response ◽  
Substantial Progress ◽  
Eeg Recordings ◽  
The Brain

Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.

scholarly journals Holding a group together: non-game-theory vs. game-theory

2021 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Competitive Equilibrium ◽  
Solution Concept ◽  
Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

scholarly journals Duopoly price competition with limited capacity

2021 ◽  
Author(s):  
A. Bërdëllima
Keyword(s):  
Price Competition ◽  
Small Firms ◽  
Common Knowledge ◽  
Limited Capacity ◽  
Equilibrium Outcome ◽  
Second Stage ◽  
Duopoly Model ◽  
Full Capacity ◽  
Stage Game ◽  
The Given

AbstractWe study a variation of the duopoly model by Kreps and Scheinkman (1983). Firms limited by their capacity of production engage in a two stage game. In the first stage they commit to levels of production not exceeding their capacities which are then made common knowledge. In the second stage after production has taken place firms simultane- ously compete in prices. Solution of this sequential game shows that the unique Cournot equilibrium outcome as in Kreps and Scheinkman is not always guaranteed. However the Cournot outcome is still robust in the sense that given sufficiently large capacities this equilibrium holds. If capacities are sufficiently small, firms decide to produce at their full capacity and set a price which clears the market at the given level of output.

Economies with complex property rights

2021 ◽  
Vol 19 (1) ◽  
pp. 30-44
Author(s):  
Ivan Balbuzanov ◽  
Maciej H. Kotowski
Keyword(s):  
Property Rights ◽  
Solution Concept ◽  
Object Allocation ◽  
Top Trading Cycles ◽  
The Right ◽  
Shared Ownership

We discuss the exclusion core, a solution concept for object-allocation and object-exchange problems. The exclusion core is based on the right of exclusion and is especially useful for the analysis of economies with complicated property arrangements, such as those with shared ownership. The exclusion core coincides with the (strong) core in classic settings, and is closely related to the celebrated Top Trading Cycles algorithm.

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