On the characterization of weighted simple games

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.     

Asymmetric Choquet random walks and ambiguity aversion or seeking

Asymmetric Choquet random walks are defined, in the form of dynamically consistent random walks allowing for asymmetric conditional capacities. By revisiting Kast and Lapied (Dynamically consistent Choquet random walk and real investments. Document de Travail n. 2010-33, GREQAM, HAL id: halhs-00533826, 2010b) and Kast et al. (Econ Model, 38:495–503, 2014) we show that some findings regarding the effects of ambiguity aversion are preserved in the more general framework, which is of interest in several applications to policy making, risk management, corporate decisions, real option valuation of investment/ disinvestment projects, etc. The effect of ambiguity on the higher moments is investigated, as well, as they have an interpretation in terms of the psychological attitude of a decision-maker towards ambiguity. Finally, some financial applications are provided as an illustration.     

Resolute majority rules

We investigate resolute voting rules that always rank two alternatives strictly and avoid social indecision. Resolute majority rules differ from the standard majority rule in that whenever both alternatives win the same number of votes, a tie-breaking function is used to determine the outcome. We provide axiomatic characterizations of resolute majority rules or resolute majority rules with a quorum. Resoluteness axiom is used in all these results. The other axioms are weaker than those considered in the characterization of the majority rule by May (1952 Econometrica, 20:680–684). In particular, instead of May’s positive responsiveness, we consider a much weaker monotonicity axiom.     

A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting

The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans (Econometrica 28(2):287–309, 1960, 1972) and Koopmans et al. (Econometrica 32(1/2):82–100, 1964) with subsequent contributions by several other authors, including Bleichrodt et al. (J Math Psychol 52(6):341–347, 2008). The papers by Hayashi (J Econ Theory 112(2):343–352, 2003) and Olea and Strzalecki (Q J Econ 129(3):1449–1499, 2014) axiomatize quasi-hyperbolic discounting. The main contribution of this paper is to provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn (The foundations of expected utility. Reidel Publishing Co, Dordrecht, 1982) and Harvey (Manag Sci 32(9):1123–1139, 1986), we show that Anscombe and Aumann’s (Ann Math Stat 34(1):199–205, 1963) version of Subjective Expected Utility theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.     

Dynamic awareness and zero probability beliefs

We study behavioral patterns of insurance demand for low-probability large-loss events (catastrophic losses). Individual patterns of belief formation and risk attitude that were suggested in the behavioral decisions literature emerge robustly in the current set of insurance choices. However, social comparison effects are less robust. We do not find any evidence for peer effects (through social-loss aversion or imitation) on insurance take-up. In contrast, we find support for the prediction that people underweight others’ relevant information in their own decision making.     

A note on budget constraints and outside options in common agency

Bernheim and Whinston (Q J Econ 101:1–31, 1986) show that, in a common agency problem without budget constraints, the set of Nash equilibria with truthful strategies (TNE), the set of coalition-proof Nash equilibria (CPNE), and the principal-optimal core of the underlying coalitional game are non-empty and all equivalent in payoff space. We show that, with budget constraints, none of Bernheim and Whinston’s (Q J Econ 101:1–31, 1986) results hold: (i) a CPNE may not exist, (ii) a TNE may not exist even when a CPNE exists, (iii) a TNE may not be a CPNE, and (iv) both TNE and CPNE payoffs are core allocations but are not necessarily principal-optimal. However, when principals have outside options but no budget constraints, (i), and (iii) continue to hold but not for (ii) and (iv). In particular, a TNE always exists but the core may be empty.     

(Sub) Optimality and (non) optimal satisficing in risky decision experiments

We implement a risky choice experiment based on one-dimensional choice variables and risk neutrality induced via binary lottery incentives. Each participant confronts many parameter constellations with varying optimal payoffs. We assess (sub)optimality, as well as (non)optimal satisficing by eliciting aspirations in addition to choices. Treatments differ in the probability that a binary random event, which are payoff—but not optimal choice—relevant is experimentally induced and whether participants choose portfolios directly or via satisficing, i.e., by forming aspirations and checking for satisficing before making their choice. By incentivizing aspiration formation, we can test satisficing, and in cases of satisficing, determine whether it is optimal.     

Meaningful learning in weighted voting games: an experiment

In April 2013, all of the major academic publishing houses moved thousands of journal titles to an original hybrid model, under which authors of accepted papers can choose between an expensive open access (OA) track and the traditional track available only to subscribers. This paper argues that authors might now use a publication strategy as a quality signaling device. The imperfect information game between authors and readers presents several types of Perfect Bayesian Equilibria, including a separating equilibrium in which only authors of high-quality papers are driven toward the open access track. The publishing house should choose an open-access publication fee that supports the emergence of the highest return equilibrium. Journal structures will evolve over time according to the journals’ accessibility and quality profiles.     

A note on mixingale limit theorems and stable convergence in law

A gap in the proof of a non stationary mixingale invariance principle is identified and fixed by introducing a skipped subsampling of a partial sum process and letting the skipped interval vanish asymptotically at an appropriate rate as the sample size increases. The corrected proof produces a mixingale limit theorem in the form of a mixing convergence in law, occurring jointly with the stable convergence in law for the same σ-field relative to which they are stable and mixing. The applicability of established results to a high-frequency estimation of the quadratic variation of financial price process is discussed.     

Parallel and interacting stochastic approximation annealing algorithms for global optimisation

We present the parallel and interacting stochastic approximation annealing (PISAA) algorithm, a stochastic simulation procedure for global optimisation, that extends and improves the stochastic approximation annealing (SAA) by using population Monte Carlo ideas. The efficiency of standard SAA algorithm crucially depends on its self-adjusting mechanism which presents stability issues in high dimensional or rugged optimisation problems. The proposed algorithm involves simulating a population of SAA chains that interact each other in a manner that significantly improves the stability of the self-adjusting mechanism and the search for the global optimum in the sampling space, as well as it inherits SAA desired convergence properties when a square-root cooling schedule is used. It can be implemented in parallel computing environments in order to mitigate the computational overhead. As a result, PISAA can address complex optimisation problems that it would be difficult for SAA to satisfactory address. We demonstrate the good performance of the proposed algorithm on challenging applications including Bayesian network learning and protein folding. Our numerical comparisons suggest that PISAA outperforms the simulated annealing, stochastic approximation annealing, and annealing evolutionary stochastic approximation Monte Carlo.