scholarly journals Partial Order Games

Games ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 2
Author(s):  
Valeria Zahoransky ◽  
Julian Gutierrez ◽  
Paul Harrenstein ◽  
Michael Wooldridge
Keyword(s):  
Partial Order ◽  
Imperfect Information ◽  
Compact Representation ◽  
Game Model ◽  
Extensive Form ◽  
Dependence Relation ◽  
Extensive Form Games ◽  
Extensive Form Game ◽  
The Cost ◽  
The Relationship

We introduce a non-cooperative game model in which players’ decision nodes are partially ordered by a dependence relation, which directly captures informational dependencies in the game. In saying that a decision node v is dependent on decision nodes v1,…,vk, we mean that the information available to a strategy making a choice at v is precisely the choices that were made at v1,…,vk. Although partial order games are no more expressive than extensive form games of imperfect information (we show that any partial order game can be reduced to a strategically equivalent extensive form game of imperfect information, though possibly at the cost of an exponential blowup in the size of the game), they provide a more natural and compact representation for many strategic settings of interest. After introducing the game model, we investigate the relationship to extensive form games of imperfect information, the problem of computing Nash equilibria, and conditions that enable backwards induction in this new model.

scholarly journals Solving Large Extensive-Form Games with Strategy Constraints

2019 ◽  
Vol 33 ◽  
pp. 1861-1868
Author(s):  
Trevor Davis ◽  
Kevin Waugh ◽  
Michael Bowling
Keyword(s):  
Private Information ◽  
Imperfect Information ◽  
Risk Mitigation ◽  
Solution Concept ◽  
Optimal Strategies ◽  
Linear Constraints ◽  
Convex Constraints ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Large Extensive Form Games

Extensive-form games are a common model for multiagent interactions with imperfect information. In two-player zerosum games, the typical solution concept is a Nash equilibrium over the unconstrained strategy set for each player. In many situations, however, we would like to constrain the set of possible strategies. For example, constraints are a natural way to model limited resources, risk mitigation, safety, consistency with past observations of behavior, or other secondary objectives for an agent. In small games, optimal strategies under linear constraints can be found by solving a linear program; however, state-of-the-art algorithms for solving large games cannot handle general constraints. In this work we introduce a generalized form of Counterfactual Regret Minimization that provably finds optimal strategies under any feasible set of convex constraints. We demonstrate the effectiveness of our algorithm for finding strategies that mitigate risk in security games, and for opponent modeling in poker games when given only partial observations of private information.

scholarly journals An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information

2014 ◽  
Vol 51 ◽  
pp. 829-866 ◽  
Author(s):  
B. Bosansky ◽  
C. Kiekintveld ◽  
V. Lisy ◽  
M. Pechoucek
Keyword(s):  
Nash Equilibrium ◽  
Imperfect Information ◽  
Search Algorithm ◽  
Main Idea ◽  
Substantial Improvement ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Solution Algorithms ◽  
Restricted Game ◽  
Zero Sum

Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the compact sequence-form representation of extensive-form games and (2) the algorithmic framework of double-oracle methods. The main idea of our algorithm is to restrict the game by allowing the players to play only selected sequences of available actions. After solving the restricted game, new sequences are added by finding best responses to the current solution using fast algorithms. We experimentally evaluate our algorithm on a set of games inspired by patrolling scenarios, board, and card games. The results show significant runtime improvements in games admitting an equilibrium with small support, and substantial improvement in memory use even on games with large support. The improvement in memory use is particularly important because it allows our algorithm to solve much larger game instances than existing linear programming methods. Our main contributions include (1) a generic sequence-form double-oracle algorithm for solving zero-sum extensive-form games; (2) fast methods for maintaining a valid restricted game model when adding new sequences; (3) a search algorithm and pruning methods for computing best-response sequences; (4) theoretical guarantees about the convergence of the algorithm to a Nash equilibrium; (5) experimental analysis of our algorithm on several games, including an approximate version of the algorithm.

scholarly journals Contractual incompleteness in an extensive-form game under perfect information using Stackelberg model

2014 ◽  
Vol 3 (2) ◽  
Author(s):  
Anton Abdulbasah Kamil
Keyword(s):  
General Class ◽  
Perfect Information ◽  
Financial Contracts ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Form Game ◽  
Strategic Default ◽  
Contractual Incompleteness ◽  
Extensive Form Game ◽  
Stackelberg Model

The paper presents the explanation of contractual commitments which are renegotiation-proof, based on “strategic default”. Under this, financial contracts must provide incentives of their own so that the parties would honor the agreement. We investigates the reach of this type of commitment within the general class of extensive form games. The result is that a renegotiation-proof contract exists which commits against every deviation from the equilibrium which would induce a revenue acceleration. AMS Subj. Classification: 91A40, 91A20 .

scholarly journals A Game-Theoretic Account of Responsibility Allocation

2021 ◽  
Author(s):  
Christel Baier ◽  
Florian Funke ◽  
Rupak Majumdar
Keyword(s):  
Imperfect Information ◽  
Fundamental Problem ◽  
Multi Agent Systems ◽  
Extensive Form ◽  
Responsibility Attribution ◽  
Agent Interaction ◽  
Responsibility Ascription ◽  
Multi Agent ◽  
Game Theoretic ◽  
Extensive Form Game

When designing or analyzing multi-agent systems, a fundamental problem is responsibility ascription: to specify which agents are responsible for the joint outcome of their behaviors and to which extent. We model strategic multi-agent interaction as an extensive form game of imperfect information and define notions of forward (prospective) and backward (retrospective) responsibility. Forward responsibility identifies the responsibility of a group of agents for an outcome along all possible plays, whereas backward responsibility identifies the responsibility along a given play. We further distinguish between strategic and causal backward responsibility, where the former captures the epistemic knowledge of players along a play, while the latter formalizes which players – possibly unknowingly – caused the outcome. A formal connection between forward and backward notions is established in the case of perfect recall. We further ascribe quantitative responsibility through cooperative game theory. We show through a number of examples that our approach encompasses several prior formal accounts of responsibility attribution.

scholarly journals Decentralized No-regret Learning Algorithms for Extensive-form Correlated Equilibria (Extended Abstract)

2021 ◽  
Author(s):  
Andrea Celli ◽  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Nicola Gatti
Keyword(s):  
Normal Form ◽  
Private Information ◽  
Imperfect Information ◽  
Research Question ◽  
Correlated Equilibrium ◽  
Extensive Form ◽  
Learning Dynamics ◽  
Extensive Form Games ◽  
Normal Form Games ◽  
Correlated Equilibria

The existence of uncoupled no-regret learning dynamics converging to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normal-form game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensive-form games generalize normal-form games by modeling both sequential and simultaneous moves, as well as imperfect information. Because of the sequential nature and the presence of private information, correlation in extensive-form games possesses significantly different properties than in normal-form games. The extensive-form correlated equilibrium (EFCE) is the natural extensive-form counterpart to the classical notion of correlated equilibrium in normal-form games. Compared to the latter, the constraints that define the set of EFCEs are significantly more complex, as the correlation device ({\em a.k.a.} mediator) must take into account the evolution of beliefs of each player as they make observations throughout the game. Due to this additional complexity, the existence of uncoupled learning dynamics leading to an EFCE has remained a challenging open research question for a long time. In this article, we settle that question by giving the first uncoupled no-regret dynamics which provably converge to the set of EFCEs in n-player general-sum extensive-form games with perfect recall. We show that each iterate can be computed in time polynomial in the size of the game tree, and that, when all players play repeatedly according to our learning dynamics, the empirical frequency of play after T game repetitions is guaranteed to be a O(T^-1/2)-approximate EFCE with high probability, and an EFCE almost surely in the limit.

Extensive Form Rationalizability

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Common Knowledge ◽  
Backward Induction ◽  
Forward Induction ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Dominated Strategies ◽  
Extensive Form Game ◽  
Common Knowledge Of Rationality

The extensive form of a game is informationally richer than the normal form since players gather information that allows them to update their subjective priors as the game progresses. For this reason, the study of rationalizability in extensive form games is more complex than the corresponding study in normal form games. There are two ways to use the added information to eliminate strategies that would not be chosen by a rational agent: backward induction and forward induction. The latter is relatively exotic (although more defensible). Backward induction, by far the most popular technique, employs the iterated elimination of weakly dominated strategies, arriving at the subgame perfect Nash equilibria—the equilibria that remain Nash equilibria in all subgames. An extensive form game is considered generic if it has a unique subgame perfect Nash equilibrium. This chapter develops the tools of modal logic and presents Robert Aumann's famous proof that common knowledge of rationality (CKR) implies backward induction. It concludes that Aumann is perfectly correct, and the real culprit is CKR itself. CKR is in fact self-contradictory when applied to extensive form games.

The Awareness Level of the Safety and Health of the Operational Level

2017 ◽  
Vol 3 (1) ◽  
pp. 42
Author(s):  
Roshanira Che Mohd Noor ◽  
Nur Atiqah Rochin Demong
Keyword(s):  
Health And Safety ◽  
Health Conditions ◽  
Effective Strategies ◽  
Operational Level ◽  
Safety And Health ◽  
Health Factors ◽  
The Cost ◽  
The Relationship ◽  
Awareness Level

Providing a safe and healthy workplace is one of the most effective strategies in for holding down the cost of doing construction business. It was a part of the overall management system to facilitate themanagement of the occupational health and safety risk that are associated with the business of the organization. Factors affected the awareness level inclusive of safety and health conditions, dangerous working area, long wait care and services and lack of emergency communication werethe contributed factors to the awareness level for the operational level. Total of 122 incidents happened at Telekom Malaysia Berhad as compared to year 2015 only 86 cases. Thus, the main objective of this study was to determine the relationship between safety and health factors and the awareness level among operational workers.The determination of this research was to increase the awareness level among the operational level workerswho committing to safety and health environment.

Pound Wise and Penny Foolish? Weight Loss and The Dynamics of Health Care Spending

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Thomas G Koch
Keyword(s):  
Weight Loss ◽  
Cost Savings ◽  
Cost Effective ◽  
Economic Consequences ◽  
Health Care Spending ◽  
Order Of Magnitude ◽  
Dynamic Measures ◽  
The Cost ◽  
The Impact ◽  
The Relationship

Current estimates of obesity costs ignore the impact of future weight loss and gain, and may either over or underestimate economic consequences of weight loss. In light of this, I construct static and dynamic measures of medical costs associated with body mass index (BMI), to be balanced against the cost of one-time interventions. This study finds that ignoring the implications of weight loss and gain over time overstates the medical-cost savings of such interventions by an order of magnitude. When the relationship between spending and age is allowed to vary, weight-loss attempts appear to be cost-effective starting and ending with middle age. Some interventions recently proven to decrease weight may also be cost-effective.

Marginal assessment of the cost and benefits of aphasia treatment: Evidence from community-based telerehabilitation treatment for aphasia

2021 ◽  
pp. 1357633X2098277
Author(s):  
Molly Jacobs ◽  
Patrick M Briley ◽  
Heather Harris Wright ◽  
Charles Ellis
Keyword(s):  
Cost Effectiveness ◽  
Economies Of Scale ◽  
Reference Group ◽  
Unit Cost ◽  
Community Based ◽  
Face To Face ◽  
Conduction Aphasia ◽  
Aphasia Treatment ◽  
The Cost ◽  
The Relationship

Introduction Few studies have reported information related to the cost-effectiveness of traditional face-to-face treatments for aphasia. The emergence and demand for telepractice approaches to aphasia treatment has resulted in an urgent need to understand the costs and cost-benefits of this approach. Methods Eighteen stroke survivors with aphasia completed community-based aphasia telerehabilitation treatment, utilizing the Language-Oriented Treatment (LOT) delivered via Webex videoconferencing program. Marginal benefits to treatment were calculated as the change in Western Aphasia Battery-Revised (WAB-R) score pre- and post-treatment and marginal cost of treatment was calculated as the relationship between change in WAB-R aphasia quotient (AQ) and the average cost per treatment. Controlling for demographic variables, Bayesian estimation evaluated the primary contributors to WAB-R change and assessed cost-effectiveness of treatment by aphasia type. Results Thirteen out of 18 participants experienced significant improvement in WAB-R AQ following telerehabilitation delivered therapy. Compared to anomic aphasia (reference group), those with conduction aphasia had relatively similar levels of improvement whereas those with Broca’s aphasia had smaller improvement. Those with global aphasia had the largest improvement. Each one-point of improvement cost between US$89 and US$864 for those who improved (mean = US$200) depending on aphasia type/severity. Discussion Individuals with severe aphasia may have the greatest gains per unit cost from treatment. Both improvement magnitude and the cost per unit of improvement were driven by aphasia type, severity and race. Economies of scale to aphasia treatment–cost may be minimized by treating a variety of types of aphasia at various levels of severity.

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