242 research outputs found
Conditional Belief Types
No full textWe study type spaces where a player’s type at a state is a conditional probability on the space. We axiomatize these spaces using conditional belief operators, examining three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certain of her beliefs. Second, echo, according to which the unconditional beliefs implied by the condition must be held given the condition. Third, determination, which says that the conditional beliefs are the unconditional beliefs that are conditionally certain. Echo implies that conditioning on an event is the same as conditioning on the event being certain, which formalizes the standard informal interpretation of conditional probability. The game-theoretic application of our model, discussed within an example, sheds light on a number of issues in the analysis of extensive form games. Type spaces are closely related to the sphere models of counterfactual conditionals and to models of hypothetical knowledge
Reasoning about Interaction: From Game Theory to Logic and Back (Dagstuhl Seminar 11101)
No full textThis report documents the program and the outcomes of Dagstuhl Seminar 11101 ``Reasoning about Interaction: From Game Theory to Logic and Back''.
The notion of interaction is crucial in several disciplines, including
social science, operational research, and
economics. Two frameworks are most prominent in the formal treatment of
interaction: game theory and mathematical logic. Quantitative analysis is
usually conducted using models and tools of game theory. At the same time,
logic provides vocabulary and methods to study interaction in a qualitative
way.
The aim of the seminar was to bring together researchers who approach
interaction-related phenomena from different perspectives (and with
different conceptual tools). We hoped that, by synergy and exchange of
expertise, a more integrative view of interaction could be obtained. In particular, we focussed on how interaction between individual entities (be it humans, robots and/or virtual creatures) can lead to emergence of social structures, collective behavior, and teamwork - and, ultimately, help all involved parties benefit from cooperation
Monologues, dialogues, and common priors
No full textThe main purpose of this paper is to provide a simple criterion enabling to conclude that two agents do not share a common prior. The criterion is simple, as it does not require information about the agents' knowledge and beliefs, but rather only the record of a dialogue between the agents. In each stage of the dialogue the agents tell each other the probability they ascribe to a fixed event and update their beliefs about the event. To characterize dialogues consistent with a common prior, we first study monologues, which are sequences of probabilities assigned by a single agent to a given event in an exogenous learning process. A dialogue is consistent with a common prior if and only if each selection sequence from the two monologues comprising the dialogue is itself a monologue
Unawareness, Beliefs and Games
No full textWe define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We use our unawareness belief structure to show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized “No-trade” theorem according to which there can not be common certainty of strict preference to trade. Moreover, we show a generalization of the “No-agreeing-to-disagree” theorem
What if Achilles and the tortoise were to bargain? An argument against interim agreements
No full textZeno's paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement is concerned. Parkinson's Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements and using arguments similar to Zeno's, we show that if utilities are von Neumann-Morgenstern, then no such process can bring about an agreement in finite time in linear bargaining problems. To extend this result for all bargaining problems, we characterize a particular path illustrated by \cite{ra}, and show that no agreement is reached along this path in finite time.Zeno's paradox, bargaining problems, interim agreements, vNM utility
Topology-Free Typology of Beliefs
No full textIn their seminal paper, Mertens and Zamir (1985) proved the existence of a universal Harsanyi type space which consists of all possible types. Their method of proof depends crucially on topological assumptions. Whether such assumptions are essential to the existence of a universal space remained an open problem. We answer it here by proving that a universal type space does exist even when spaces are defined in pure measure theoretic terms. Heifetz and Samet (1996) showed that coherent hierarchies of beliefs, in the measure theoretic case, do not necessarily describe types. Therefore, the universal space here differs from all previously studied ones, in that it does not necessarily consist of all coherent hierarchies of beliefs.Harsanyi types, Universal type spaces
Valuation Equilibria
No full textWe introduce a new solution concept for games in extensive form with perfect information: the valuation equilibrium. The moves of each player are partitioned into similarity classes. A valuation of the player is a real valued function on the set of her similarity classes. At each node a player chooses a move that belongs to a class with maximum valuation. The valuation of each player is \emph{consistent} with the strategy profile in the sense that the valuation of a similarity class is the player expected payoff given that the path (induced by the strategy profile) intersects the similarity class. The solution concept is applied to decision problems and multi-player extensive form games. It is contrasted with existing solution concepts. An aspiration-based approach is also proposed, in which the similarity partitions are determined endogenously. The corresponding equilibrium is called the aspiration-based valuation equilibrium (ASVE). While the Subgame Perfect Nash Equilibrium is always an ASVE, there are other ASVE in general. But, in zero-sum two-player games without chance moves every player must get her value in any ASVE.bounded rationality, valuation, similarity, aspiration.
Pseudo Picard Operators On Generalized Metric Spaces
No full textAltun, Ishak/0000-0002-7967-0554; Samet, Bessem/0000-0002-6769-3417In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. JLELI AND B. SAMET: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result.Deanship of Scientific Research at King Saud UniversityDeanship of Scientific Research at King Saud University [RGP-237]The second author extends his appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No RGP-237
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