THE ROBUSTNESS OF EQUILIBRIUM ANALYSIS: THE CASE OF UNDOMINATED NASH EQUILIBRIUM

I consider a strategic game form with a finite set of payoff states and employ undominated Nash equilibrium (UNE) as a solution concept under complete information. I propose notions of the proximity of information according to which the continuity of UNE concept is considered as the robustness criterion. I identify a topology (induced by what I call d?) with respect to which the undominated Bayesian Nash equilibrium (UBNE) correspondence associated with any game form is upper hemi-continuous at any complete information prior. I also identify a slightly coarser topology (induced by what I call d??) with respect to which the UBNE correspondence associated with some game form exhibits a failure of the upper hemi-continuity at any complete information prior. In this sense, the topology induced by d? is the coarsest one. The topology induced by d?? is also used in both Kajii and Morris (1998) and Monderer and Samet (1989, 1996) with some additional restriction. I apply this robustness analysis to the UNE implementation. Appealing to Palfrey and Srivastava’s (1991) canonical game form, I show, as a corollary, that almost any social choice function is robustly UNE implementable relative to d?. I show, on the other hand, that only monotonic social choice functions can be robustly UNE implementable relative to d??. This clarifies when Chung and Ely’s Theorem 1 2003) applies.

A New Necessary Condition for Implementation in Iteratively Undominated Strategies

Implementation in iteratively undominated strategies relies on permissive conditions. However, for the sufficiency results available, authors have relied on assumptions that amount to quasilinear preferences on a numeraire. We uncover a new necessary condition that implies that such assumptions cannot be dispensed with. We term the condition “restricted deceptionproofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation are more restrictive than previously thought.mechanism design; exact and approximate implementation; iteratively undominated strategies; restricted deception-proofness; incentive compatibility; measurability

A new necessary condition for implementation in iteratively undominated strategies

Implementation in iteratively undominated strategies relies on permissive conditions. However, for the sufficiency results available, authors have relied on assumptions that amount to quasilinear preferences on a numeraire. We uncover a new necessary condition that implies that such assumptions cannot be dispensed with. We term the condition “restricted deception-proofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation are more restrictive than previously thought.mechanism design; exact and approximate implementation; iteratively undominated strategies; restricted deception-proofness; incentive compatibility; measurability

Evaluating the Conditions for Robust Mechanism Design Abstract: We assess the strength of the different conditions identified in the literature of robust mechanism design. We focus on three conditions: ex post incentive compatibility, robust monotonicity, and robust measurability. Ex post incentive compatibility has been shown to be necessary for any concept of robust implementation, while robust monotonicity and robust measurability have been shown to be necessary for robust (full) exact and virtual implementation, respectively. This paper shows that while violations of ex post incentive compatibility and robust monotonicity do not easily go away, we identify a mild condition on environments in which robust measurability is satisfied by all social choice functions over an open and dense subset of first-order types. We conclude that there is a precise sense in which robust virtual implementation can be significantly more permissive than robust exact implementation.

robust mechanism design; ex post incentive compatibility; robust monotonicity; robust measurability

Why two makes it more attractive than just with one... or Bianchi class-A models and Reissner-Nordstr\"om Black Holes in Quantum N=2 Supergravity

Bianchi class-A models and Reissner-Nordst\"rom (RN) black hole scenarios are considered from the point of view of quantum N=2 Supergravity. It is shown that the presence of Maxwell fields in the supersymmetry constraints implies a non-conservation of the fermion number present in Bianchi class-A models. This effect corresponds to a mixing between different (Lorentz invariant) fermionic sectors in the wave function of the Universe. Quantum states are constituted by exponentials of N=2 supersymmetric Chern-Simons functionals. With respect to the RN case, we analyse some problems and features present in a reduced model with supersymmetry. Lines of subsequent research work are then provided.Comment: 5 pages, uses ``twoside,fleqn,espcrc2'' in LaTeX, Extended version of talks/communications presented at the conferences Constrained Dynamics and Quantum Gravity, Sta. Marguerita, September 1996, Italy; New Voices in Gravitation and Quantum Gravity, Penn State, November 1996, USA and 18th Texas Symposium on Relativistic Astrophysics, December 1996, Chicago, USA; to appear in Nuc. Phys. B 1997 (Supplements

A Critical Analysis of Canada's Sex Work Legislation: Exploring Gendered and Racialized Consequences

In 2013, the Supreme Court of Canada ruled that three sections of the Criminal Code of Canada pertaining to sex work were unconstitutional. In response to this ruling—otherwise known as the Bedford Decision—the Conservative government introduced the Protection of Communities and Exploited Persons Act (PCEPA) in 2014. In this paper, I ask: to what extent does the Protection of Communities and Exploited Persons Act meet its stated goal of addressing the health and safety of those who “engage in prostitution”? In exploring this question, I first trace the legal terrain leading to the PCEPA’s conception. Following this, I show that the PCEPA has failed to address its stated goals in two central ways. First, by co-opting the progressive framing of the Bedford Decision in a way that obscures the situations of violence it seeks to address, and second, by making the most precarious category of sex work even more dangerous through its implementation. In order to render the actual foundations of the PCEPA visible, I draw upon critical race and feminist theory. Through this analysis, I show how gendered and racialized hierarchies regulate violence along and within the sex work spectrum. Overall, this paper argues that the PCEPA has failed to address the health and safety of “those engaged in prostitution,” and instead, has facilitated racialized patterns of gender violence against vulnerable populations