FRAL - Programme franco-allemand en SHS

Ambiguity in Games: The Role of Uncertainty in Strategic Interactions – AmGames

AmGames

Ambiguity in Games: The role of uncertainty in strategic interactions

Uncertainties and interactions

Uncertainty is key in many interactions among economic agents. It can be simple and repeated (one then speaks of risk) or complex and new (this is then called ambiguity). Game theory has extensively studied risky situations, both to characterize non deterministic outcomes or to characterize the nature of the actions undertaken (as it is sometimes optimal not to play a deterministic action). In this approach, risk is fully described through a probability distribution. The idea that ambiguity might be an important feature of the game is relatively new. Ambiguity is captured by a set of probability distributions. This project intended to pursue this line of research. We thus adopt this approach and assume that both strategies and beliefs of the agents can be made of sets of probability distributions.

Techniques used are those traditionally exploited in decision theory and game theory. In decision theory we follow the axiomatic approach. In game theory, we seek to provide sound definitions and characterization of strategic equilibrium. The crucial point to study ambiguity in a multi-agent framework is to specify a notion of beliefs (both on possible outcomes and on the other’s strategies). A second major issue is to study how these beliefs evolve upon arrival of information. Finally, what kind of consistency is required among beliefs and strategies is also at the heart of any equilibrium notion.

Participants to the project have written papers that can be organized around three main themes:
1/ foundations of decision and game theory;
2/ applications of game theory to economic interactions;
3/ aggregation of non-probabilistic, heterogeneous opinion.

In the first category, a god part of the work has been to work out how to revise non probabilistic beliefs upon arrival of information (e.g. the strategy of the opponent) while avoiding the well identified problem of dynamic inconsistency. The core notion aka rectangularity, allows one to generalize fundamental results of classical game theory, such as Kuhn’s theorem.
Examples of applications include the fact that ambiguity can sometimes limit the amount of information necessary to certify an action, or, to the contrary, how it can constrain messages that a public authority, say, can send to persuade an ambiguity averse agent to take a particular action.
The third category contains work that show how introducing non probabilistic beliefs allows to capture a situation in which although not consensual, the beliefs are sufficiently consistent to allow for an aggregation of them that leads to decisions that respect individuals’ preferences.

The collaboration among the partenrs continues, in particular with the co-supervision of PhD students.

Scientific production: working papers to be submitted (some of them already accepted) to international scientific journals.

Uncertainty plays a crucial role in strategic conflicts, either in the form of uncertainty of the environment or uncertainty in strategy choices. In
many real world conflicts, it is not possible to model the uncertainty by probabilistic models; instead, agents face what is called Knightian uncertainty or (model) ambiguity: the probability distribution of outcomes is not exactly known to the actors. In social conflicts, we frequently have
environmental variables as past experience, preplay communication, or cultural norms that influence the equilibrium outcome but are not directly
part of the modeled payo ffs. It is thus important to incorporate such model uncertainty or ambiguity into the analysis of strategic conflicts.
The project aims to develop a general theory of such (objective) ambiguity in strategic interactions. Two main themes will be developed. First,
in strategic conflicts it is frequently important to create uncertainty as opponents would exploit perfect information about one's behavior to one's
own detriment. Traditionally, such strategic uncertainty has been modeled by probabilistic devices with known probabilities, as dices or roulette
wheels. In real interactions, a much wider variety of strategic uncertainty is available to players. This is certainly reflected and intuitively felt in
the policy literature on negotiations and is known to bargainers alike.We take up recent advances in decision theory that allow to model such
uncertainty and study the resulting changes in equilibrium predictions for game theory. Second, the environment might itself be ambiguous. Players might not have sufficient probabilistic information over the game played, the type of the opponents etc as is traditionally assumed. In real environment,information is often scarce and does not allow probabilistic assessments. How does this uncertainty a ect the strategies played at
equilibrium? Is it possible to parametrize the set of equilibria by the degree of ambiguity of the environment? The aim of the current project
is to develop the whole theory of such situations, including its decision theoretic and epistemological foundations, the extensive form theory, and
applications to speci c strategic conflicts that are important from an economic point of view. For instance, we intend to study the consequences
of our theory for communication games or bargaining situations between economic parties. We will also accompany our studies by experiments to
test our predictions in the laboratory.

Project coordination

Jean-Marc TALLON (CENTRE D'ECONOMIE DE LA SORBONNE) – jmtallon@univ-paris1.fr

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

CES CENTRE D'ECONOMIE DE LA SORBONNE

Help of the ANR 76,200 euros
Beginning and duration of the scientific project: April 2013 - 36 Months

Useful links

Explorez notre base de projets financés

 

 

ANR makes available its datasets on funded projects, click here to find more.

Sign up for the latest news:
Subscribe to our newsletter