Incomplete information and iterated strict dominance

2020 ◽  
Author(s):  
Christian W Bach ◽  
Andrés Perea
Keyword(s):  
Incomplete Information ◽  
Solution Concept ◽  
Complete Information ◽  
Common Belief ◽  
Person Perspective ◽  
Response Sets ◽  
Best Response ◽  
Necessary And Sufficient

Abstract The solution concept of iterated strict dominance for static games with complete information recursively deletes choices that are inferior. Here, we devise such an algorithm for the more general case of incomplete information. The ensuing solution concept of generalized iterated strict dominance is characterized in terms of common belief in rationality as well as in terms of best response sets. Besides, we provide doxastic conditions that are necessary and sufficient for modelling complete information from a one-person perspective.

A Note on Rationalizability and Restrictions on Beliefs

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Giuseppe Cappelletti
Keyword(s):  
Incomplete Information ◽  
Solution Concept ◽  
Complete Information ◽  
Additional Hypothesis ◽  
Games With Incomplete Information

Rationalizability is a widely accepted solution concept in the study of strategic-form games with complete information and is fully characterized in terms of assumptions on the rationality of the players and common certainty of rationality.Battigalli and Siniscalchi extend rationalizability taking as given some exogenous restrictions on players' beliefs and derive the solution concept called ?-rationalizability. This new solution concept has been applied to games with incomplete information as well as dynamic games.On this note, I focus on games with incomplete information and characterize ?-rationalizability with a new notion of iterative dominance that is able to capture the additional hypothesis on players' beliefs.

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 Spillovers and R&D Incentive under Incomplete Information

2018 ◽  
Vol 6 (1-2) ◽  
pp. 50-65 ◽  
Author(s):  
Rittwik Chatterjee ◽  
Srobonti Chattopadhyay ◽  
Tarun Kabiraj
Keyword(s):  
Distribution Function ◽  
Incomplete Information ◽  
Private Information ◽  
Complete Information ◽  
Jel Classification ◽  
General Distribution ◽  
Two Stage ◽  
Stage Game ◽  
Alternative Scenarios

Spillovers of R&D outcome affect the R&D decision of a firm. The present paper discusses the R&D incentives of a firm when the extent of R&D spillover is private information to each firm. We construct a two-stage game involving two firms when the firms first decide simultaneously whether to invest in R&D or not, then they compete in quantity. Assuming general distribution function of firm types we compare R&D incentives of firms under alternative scenarios based on different informational structures. The paper shows that while R&D spillovers reduce R&D incentives under complete information unambiguously, however, it can be larger under incomplete information. JEL Classification: D43, D82, L13, O31

scholarly journals Bidding in Smart Grid PDAs: Theory, Analysis and Strategy

2020 ◽  
Vol 34 (02) ◽  
pp. 1974-1981
Author(s):  
Susobhan Ghosh ◽  
Sujit Gujar ◽  
Praveen Paruchuri ◽  
Easwar Subramanian ◽  
Sanjay Bhat
Keyword(s):  
Smart Grids ◽  
Complete Information ◽  
Equilibrium Analysis ◽  
Equilibrium Strategy ◽  
Double Auction ◽  
Single Shot ◽  
Wholesale Market ◽  
Bidding Strategies ◽  
Double Auctions ◽  
Best Response

Periodic Double Auctions (PDAs) are commonly used in the real world for trading, e.g. in stock markets to determine stock opening prices, and energy markets to trade energy in order to balance net demand in smart grids, involving trillions of dollars in the process. A bidder, participating in such PDAs, has to plan for bids in the current auction as well as for the future auctions, which highlights the necessity of good bidding strategies. In this paper, we perform an equilibrium analysis of single unit single-shot double auctions with a certain clearing price and payment rule, which we refer to as ACPR, and find it intractable to analyze as number of participating agents increase. We further derive the best response for a bidder with complete information in a single-shot double auction with ACPR. Leveraging the theory developed for single-shot double auction and taking the PowerTAC wholesale market PDA as our testbed, we proceed by modeling the PDA of PowerTAC as an MDP. We propose a novel bidding strategy, namely MDPLCPBS. We empirically show that MDPLCPBS follows the equilibrium strategy for double auctions that we previously analyze. In addition, we benchmark our strategy against the baseline and the state-of-the-art bidding strategies for the PowerTAC wholesale market PDAs, and show that MDPLCPBS outperforms most of them consistently.

scholarly journals Distance Metrics of D Numbers

2020 ◽  
Author(s):  
Liguo Fei ◽  
Yuqiang Feng
Keyword(s):  
Number Theory ◽  
Incomplete Information ◽  
Distance Function ◽  
Distance Measure ◽  
Complete Information ◽  
Belief Function ◽  
Distance Metrics ◽  
Modeling Methods ◽  
The Difference ◽  
D Numbers

Belief function has always played an indispensable role in modeling cognitive uncertainty. As an inherited version, the theory of D numbers has been proposed and developed in a more efficient and robust way. Within the framework of D number theory, two more generalized properties are extended: (1) the elements in the frame of discernment (FOD) of D numbers do not required to be mutually exclusive strictly; (2) the completeness constraint is released. The investigation shows that the distance function is very significant in measuring the difference between two D numbers, especially in information fusion and decision. Modeling methods of uncertainty that incorporate D numbers have become increasingly popular, however, very few approaches have tackled the challenges of distance metrics. In this study, the distance measure of two D numbers is presented in cases, including complete information, incomplete information, and non-exclusive elements

Incomplete Information in Multidimensional Databases

2003 ◽  
pp. 282-309 ◽  
Author(s):  
Cirtis E. Dyreson ◽  
Torben Bach Pedersen ◽  
Christian S. Jensen
Keyword(s):  
Incomplete Information ◽  
Complete Information ◽  
Multidimensional Data ◽  
Uncertain Information ◽  
Real World Data ◽  
Multidimensional Database ◽  
Simple Strategy ◽  
Multidimensional Databases ◽  
Derived Data ◽  
Base Data

While incomplete information is endemic to real-world data, current multidimensional data models are not engineered to manage incomplete information in base data, derived data, and dimensions. This chapter presents several strategies for managing incomplete information in multidimensional databases. Which strategy to use is dependent on the kind of incomplete information present, and also on where it occurs in the multidimensional database. A relatively simple strategy is to replace incomplete information with appropriate, complete information. The advantage of this strategy is that all multidimensional databases can manage complete information. Other strategies require more substantial changes to the multidimensional database. One strategy is to reflect the incompleteness in computed aggregates, which is possible only if the multidimensional database allows incomplete values in its hierarchies. Another strategy is to measure the amount of incompleteness in aggregated values by tallying how much uncertain information went into their production.

AMERICAN OPTIONS AND INCOMPLETE INFORMATION

2019 ◽  
Vol 22 (06) ◽  
pp. 1950035 ◽  
Author(s):  
ERIK EKSTRÖM ◽  
MARTIN VANNESTÅL
Keyword(s):  
Incomplete Information ◽  
American Options ◽  
Lower Boundary ◽  
Complete Information ◽  
Call Option ◽  
Standard Case ◽  
Underlying Process ◽  
Parameter Values ◽  
American Put

We study the optimal exercise of American options under incomplete information about the drift of the underlying process, and we show that quite unexpected phenomena may occur. In fact, certain parameter values give rise to stopping regions very different from the standard case of complete information. For example, we show that for the American put (call) option it is sometimes optimal to exercise the option when the underlying process reaches an upper (lower) boundary.

Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games

Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 693-726 ◽  
Author(s):  
Daisuke Oyama ◽  
Satoru Takahashi
Keyword(s):  
Incomplete Information ◽  
High Probability ◽  
Equilibrium Selection ◽  
Common Belief ◽  
Supermodular Games ◽  
Prior Beliefs ◽  
Global Game ◽  
Game Equilibrium ◽  
Type Spaces ◽  
Action Profile

This paper studies the robustness of an equilibrium to incomplete information in binary‐action supermodular games. Using a generalized version of belief operator, we explore the restrictions that prior beliefs impose on higher order beliefs. In particular, we obtain a nontrivial lower bound on the probability of a common belief event, uniform over type spaces, when the underlying game has a monotone potential. Conversely, when the game has no monotone potential, we construct a type space with an arbitrarily high probability event in which players never have common belief about that event. As an implication of these results, we show for generic binary‐action supermodular games that an action profile is robust to incomplete information if and only if it is a monotone potential maximizer. Our study offers new methodology and insight to the analysis of global game equilibrium selection.

Pre-contest Communication Incentives

2017 ◽  
Vol 18 (1) ◽  
Author(s):  
Mustafa Yildirim
Keyword(s):  
Incomplete Information ◽  
Complete Information ◽  
Psychological Strength

AbstractTo demonstrate resolution and psychological strength, players often engage in pre-contest communication by publicly stating their desire to win an upcoming contest. Existing explanations for this phenomenon revolve around incomplete information and signaling. In this paper, I offer a complementary explanation that does not rely on signaling. Within a complete information setup, I show that players may have an incentive for pre-contest communication if, in addition to an audience (reputational) cost when the statement does not materialize, the players also incur an audience reward (credibility gain) when the statement materializes.

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