515 research outputs found
Decidability Results for Multi-objective Stochastic Games
We study stochastic two-player turn-based games in which the objective of one
player is to ensure several infinite-horizon total reward objectives, while the
other player attempts to spoil at least one of the objectives. The games have
previously been shown not to be determined, and an approximation algorithm for
computing a Pareto curve has been given. The major drawback of the existing
algorithm is that it needs to compute Pareto curves for finite horizon
objectives (for increasing length of the horizon), and the size of these Pareto
curves can grow unboundedly, even when the infinite-horizon Pareto curve is
small. By adapting existing results, we first give an algorithm that computes
the Pareto curve for determined games. Then, as the main result of the paper,
we show that for the natural class of stopping games and when there are two
reward objectives, the problem of deciding whether a player can ensure
satisfaction of the objectives with given thresholds is decidable. The result
relies on intricate and novel proof which shows that the Pareto curves contain
only finitely many points. As a consequence, we get that the two-objective
discounted-reward problem for unrestricted class of stochastic games is
decidable.Comment: 35 page
The Efficiency of Direct Public Involvement in Environmental Policymaking: An Experimental Test
In one of the most ambitious forms of environmental decision-making, representatives of interested parties â environmentalists, developers, farmers, loggers, miners, etc. - are charged with the responsibility of developing a set of public policies that is acceptable to all of them. Although this approach has become increasingly popular, and has been widely discussed in the academic literature, little is known about the characteristics of the outcomes that are reached in this type of negotiation. We do not know, for example, whether these outcomes meet the standard criteria for efficiency or equity. In this paper, we use laboratory experiments to test whether a number of axiomatic models of bargaining can predict the behavior of the parties to environmental decision making. In recognition of the multi-dimensional aspect of most public land use conflicts, we ask pairs of subjects to negotiate over two goods, without the possibility of cash side payments. We thus provide one of the first experimental tests of a prediction associated with the Edgeworth Box: that parties with an initial endowment that is Pareto inefficient will make trades until they reach a Pareto efficient allocation. We further test whether parties in particular reach the Nash bargain when it coincides with or conflicts with outcomes that maximise the partiesâ joint payoffs and with outcomes at which the partiesâ receive equal payoffs. Finally, the effect of providing parties with full or partial information regarding payoffs is also examined.Axiomatic models of bargaining; Experimental tests; Land use conflicts; Collaborative policymaking
The Effect of Entitlements and Equality on Cooperative Bargaining with Private, Unverifiable Information
In many bargaining situations a third party is authorized to impose a backstop position on the bargainers. Prominent examples include governments who use collaborative policymaking between stakeholders to set public policy, but also compulsory arbitration in labour negotiations. Axiomatic models of cooperative bargaining, such as the Nash bargain, presume that the status quo allocation will have no effect on the outcome parties reach if it differs from the backstop set by the third party. In contrast, experimental findings have suggested that both equality of outcomes and entitlement (where the status quo establishes a focal point) may affect the agreements bargainers reach, at least under full information. This paper extends the investigation of the effect of equality and entitlement on cooperative bargaining to the case where parties have private, unverifiable information concerning the value of outcomes. We use a two-party, two-attribute experimental design in which subjects take part in unstructured, face-to-face bargaining to jointly select from among approximately 200 potential outcomes. We find that, relative to full information, parties who bargain under private information are almost as likely to reach agreements as those under full information, and that these agreements are still approximately Pareto efficient. Further, the effect of the status quo (rather than backstop) allocation seems amplified under private information, while the effect of equality is dampened, but not eliminated.cooperative bargaining; private information; Nash bargain; egalitarian; entitlement; fairness; focal points
A General Bargaining Model of Legislative Policy-making
We present a general model of legislative bargaining in which the status quo is an arbitrary point in a multidimensional policy space. In contrast to other bargaining models, the status quo is not assumed to be bad for all legislators, and delay may be Pareto efficient. We prove existence of stationary equilibria. We show that if all legislators are risk averse or if even limited transfers are possible, then delay is only possible if the status quo lies in the core. Thus, we expect immediate agreement in multidimensional models, where the core is typically empty. In one dimension, delay is possible if and only if the status quo lies in the core of the voting rule, and then it is the only possible outcome. Our comparative statics analysis yield two noteworthy insights: moderate status quos imply moderate policy outcomes, and legislative patience implies policy moderation
Unifying Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes
We consider Markov decision processes (MDPs) with multiple limit-average (or
mean-payoff) objectives. There exist two different views: (i) the expectation
semantics, where the goal is to optimize the expected mean-payoff objective,
and (ii) the satisfaction semantics, where the goal is to maximize the
probability of runs such that the mean-payoff value stays above a given vector.
We consider optimization with respect to both objectives at once, thus unifying
the existing semantics. Precisely, the goal is to optimize the expectation
while ensuring the satisfaction constraint. Our problem captures the notion of
optimization with respect to strategies that are risk-averse (i.e., ensure
certain probabilistic guarantee). Our main results are as follows: First, we
present algorithms for the decision problems which are always polynomial in the
size of the MDP. We also show that an approximation of the Pareto-curve can be
computed in time polynomial in the size of the MDP, and the approximation
factor, but exponential in the number of dimensions. Second, we present a
complete characterization of the strategy complexity (in terms of memory bounds
and randomization) required to solve our problem.Comment: Extended journal version of the LICS'15 pape
Approximating values of generalized-reachability stochastic games
Simple stochastic games are turn-based 2œ-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a conjunction of such conditions as objective. Despite a plethora of recent results on the analysis of systems with multiple objectives, the decidability of this basic problem remains open. In this paper, we present an algorithm approximating the Pareto frontier of the achievable values to a given precision. Moreover, it is an anytime algorithm, meaning it can be stopped at any time returning the current approximation and its error bound
Games on graphs with a public signal monitoring
We study pure Nash equilibria in games on graphs with an imperfect monitoring
based on a public signal. In such games, deviations and players responsible for
those deviations can be hard to detect and track. We propose a generic
epistemic game abstraction, which conveniently allows to represent the
knowledge of the players about these deviations, and give a characterization of
Nash equilibria in terms of winning strategies in the abstraction. We then use
the abstraction to develop algorithms for some payoff functions.Comment: 28 page
The Adversarial Stackelberg Value in Quantitative Games
In this paper, we study the notion of adversarial Stackelberg value for
two-player non-zero sum games played on bi-weighted graphs with the mean-payoff
and the discounted sum functions. The adversarial Stackelberg value of Player 0
is the largest value that Player 0 can obtain when announcing her strategy to
Player 1 which in turn responds with any of his best response. For the
mean-payoff function, we show that the adversarial Stackelberg value is not
always achievable but epsilon-optimal strategies exist. We show how to compute
this value and prove that the associated threshold problem is in NP. For the
discounted sum payoff function, we draw a link with the target discounted sum
problem which explains why the problem is difficult to solve for this payoff
function. We also provide solutions to related gap problems.Comment: long version of an ICALP'20 pape
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