The Strategic Use of Ambiguity

Ambiguity can be used as a strategic device in some situations. To demonstrate this, we propose and study a framework for normal form games where players can use Knightian uncertainty strategically. In such Ellsberg games, players may use Ellsberg urns in addition to the standard objective mixed strategies. We assume that players are ambiguity-averse in the sense of Gilboa and Schmeidler. While classical Nash equilibria remain equilibria in the new game, there arise new Ellsberg equilibria that can be quite different from Nash equilibria. A negotiation game with three players illustrates this finding. Another class of examples shows the use of ambiguity in mediation. We also highlight some conceptually interesting properties of Ellsberg equilibria in two person games with conflicting interests.

Ellsberg games and the strategic use of ambiguity in normal and extensive form games

Sass L. Ellsberg games and the strategic use of ambiguity in normal and extensive form games. Bielefeld: Universität Bielefeld; 2013.In this thesis I propose a framework for normal and extensive form games where players can use Knightian uncertainty strategically. In such Ellsberg games, ambiguity-averse players may render their actions objectively ambiguous by using devices such as Ellsberg urns, in addition to the standard mixed strategies. This simple change in the foundations leads to a number of interesting phenomena. While Nash equilibria remain equilibria in the extended game, there arise new Ellsberg equilibria with distinct outcomes. This happens especially in games with an information structure in which a player has the possibility to threaten his opponents. I illustrate this with the example of a negotiation game with three players. This mediated peace negotiation does not have a Nash equilibrium with peace outcome, but does have a peace equilibrium when ambiguity is a possible strategy. That a game with more than two players can have interesting non-Nash Ellsberg equilibria is traced back to results on subjective equilibria. Ellsberg equilibria are mathematically characterized by the Principle of Indifference in Distributions. In an Ellsberg equilibrium, players are indifferent between all mixed strategies contained in the Ellsberg equilibrium strategy. Furthermore, I observe that in two-player games players can immunize against strategic ambiguity by playing their maximin strategy (if a completely mixed Nash equilibrium exists). I analyze Ellsberg equilibria in two-person games with common and conflicting interests. I provide a number of examples and general results how to determine the Ellsberg equilibria of these games. The equilibria of conflicting interest games (modified Matching Pennies) turn out to be consistent with experimental deviations from Nash equilibrium play. Finally, I define extensive form Ellsberg games. Under the assumption of dynamically consistent (rectangular) Ellsberg strategies, I prove a result analog to Kuhn’s theorem: rectangular Ellsberg strategies and Ellsberg behavior strategies are equivalent

Kuhn's Theorem for Extensive Form Ellsberg Games

Sass L. Kuhn's Theorem for Extensive Form Ellsberg Games. Center for Mathematical Economics Working Papers. Vol 478. Bielefeld: Center for Mathematical Economics; 2013.Riedel and Sass (2013) propose a framework for normal form games where players can use imprecise probabilistic devices. We extend this strategic use of objective ambiguity to extensive form games. We show that with rectangularity of Ellsberg strategies we have dynamic consistency in the sense of Kuhn (1953): rectangular Ellsberg strategies are equivalent to Ellsberg behavior strategies. We provide an example for our result and define Ellsberg equilibrium in such extensive form Ellsberg games

The strategic use of ambiguity

Riedel F, Sass L. The strategic use of ambiguity. Working Papers. Institute of Mathematical Economics. Vol 452. Bielefeld: Center for Mathematical Economics; 2011.Ambiguity can be used as a strategic device in some situations. To demonstrate this, we propose and study a framework for normal form games where players can use Knightian uncertainty strategically. In such Ellsberg games, players may use Ellsberg urns in addition to the standard objective mixed strategies. We assume that players are ambiguity-averse in the sense of Gilboa and Schmeidler. While classical Nash equilibria remain equilibria in the new game, there arise new Ellsberg equilibria that can be quite different from Nash equilibria. A negotiation game with three players illustrates this finding. Another class of examples shows the use of ambiguity in mediation. We also highlight some conceptually interesting properties of Ellsberg equilibria in two person games with conflicting interests

Kuhn's Theorem for Extensive Form Ellsberg Games

Mouraviev I, Riedel F, Sass L. Kuhn's Theorem for Extensive Form Ellsberg Games. Center for Mathematical Economics Working Papers. Vol 510. Bielefeld: Center for Mathematical Economics; 2014.The paper generalizes Kuhn's Theorem to extensive form games in which players condition their play on the realization of ambiguous randomization devices and use a maxmin decision rule to evaluate the consequences of their decisions. It proves that ambiguous behavioral and ambiguous mixed strate- gies are payoff-and outcome equivalent only if the latter strategies satisfy a rectangularity condition. The paper also discusses dynamic consistency. In particular, it shows that not only the profile of ambiguous strategies must be appropriately chosen but also the extensive form must satisfy further re- strictions beyond those implied by perfect recall in order to ensure that each player respects her ex ante contingent choice with the evolution of play

Inward and Outward FDI Country Profiles, Second Edition

This second edition contains a series of 77 standardized country profiles dealing with the inward and outward foreign direct investment (FDI) performance of 40 economies. The profiles have been peer-reviewed by a global network of experts. The publication is intended to contribute to the analysis of trends in foreign direct investment and policy issues related to them. More specifically, the individual profiles discuss FDI trends and developments (country-level developments, the corporate players); effects of the recent global crises; and the policy scene. Each profile contains a standard set of tables, including on FDI stocks and flows, sectoral and geographical FDI distributions, the largest M&As and greenfield investments, the principal foreign affiliates (for inward FDI), and the principal multinational enterprises (for outward FDI). The standardized template used to produce the profiles allows cross-country comparisons. The volume is meant to be a reference tool for anyone interested in foreign direct investment

International genome-wide meta-analysis identifies new primary biliary cirrhosis risk loci and targetable pathogenic pathways.

Primary biliary cirrhosis (PBC) is a classical autoimmune liver disease for which effective immunomodulatory therapy is lacking. Here we perform meta-analyses of discovery data sets from genome-wide association studies of European subjects (n=2,764 cases and 10,475 controls) followed by validation genotyping in an independent cohort (n=3,716 cases and 4,261 controls). We discover and validate six previously unknown risk loci for PBC (Pcombined<5 × 10(-8)) and used pathway analysis to identify JAK-STAT/IL12/IL27 signalling and cytokine-cytokine pathways, for which relevant therapies exist