The job search problem as an employer–candidate game

In the standard job search problem a single decision-maker (say an employer) has to choose from a sequence of candidates of varying fitness. We extend this formulation to allow both employers and candidates to make choices. We consider an infinite population of employers and an infinite population of candidates. Each employer interviews a (possibly infinite) sequence of candidates for a post and has the choice of whether or not to offer a candidate the post. Each candidate is interviewed by a (possibly infinite) sequence of employers and can accept or reject each offer. Each employer seeks to maximise the fitness of the candidate appointed and each candidate seeks to maximise the fitness of their eventual employer. We allow both discounting and/or a cost per interview. We find that there is a unique pair of policies (for employers and candidates respectively) which is in Nash equilibrium. Under these policies each population is partitioned into a finite or countable sequence of subpopulations, such that an employer (candidate) in a given subpopulation ends up matched with the first candidate (employer) encountered from the corresponding subpopulation. In some cases the number of non-empty subpopulations in the two populations will differ and some members of one population will never be matched.

Download Full-text

The job-search problem with competition: an evolutionarily stable dynamic strategy

Advances in Applied Probability ◽

10.2307/1427655 ◽

1993 ◽

Vol 25 (2) ◽

pp. 314-333 ◽

Cited By ~ 18

Author(s):

E. J. Collins ◽

J. M. Mcnamara

Keyword(s):

Job Search ◽

Evolutionarily Stable Strategy ◽

The Other ◽

Control Limit ◽

Search Problem ◽

Limit Function ◽

Reward Function ◽

Infinite Population ◽

Optimal Value ◽

Evolutionarily Stable

We consider a game-theoretical solution for an optimal stopping problem which we describe in terms of a job-search problem with an infinite population of candidates and an infinite population of posts of varying value. Each candidate finds posts from the post population at unit rate. If a post found is still vacant, a candidate can either accept it or reject it. The reward to a candidate is the value of the post if one is accepted and zero if he never accepts a post. There are no costs for searching, no discounting of future rewards and no recall of previously found posts. The only pressure on a candidate to accept a post comes from the changing rate at which he finds vacant posts (and the values associated with them) as a result of the actions of the other candidates. It is not possible to define optimality for a single candidate without reference to the policies followed by the other candidates. We say a policy π is an evolutionarily stable strategy (ESS) if it has the following property: if all candidates used π and an individual candidate was given the option of changing his policy, then it would not be to his advantage to do so. We first find the optimal value function and optimal policy for the case of a single candidate operating in an environment where the distribution of posts on offer and the chance of finding one both vary with time in a known way. We then show that for the infinite population there is a unique ESS given by a control-limit policy π c, where the control-limit function c is the solution of a given differential equation with a given initial condition. This function c also gives the expected future reward function for any single candidate when all candidates use π c.

Download Full-text

The job-search problem with competition: an evolutionarily stable dynamic strategy

Advances in Applied Probability ◽

10.1017/s0001867800025374 ◽

1993 ◽

Vol 25 (02) ◽

pp. 314-333 ◽

Cited By ~ 4

Author(s):

E. J. Collins ◽

J. M. Mcnamara

Keyword(s):

Job Search ◽

Evolutionarily Stable Strategy ◽

The Other ◽

Control Limit ◽

Search Problem ◽

Limit Function ◽

Reward Function ◽

Infinite Population ◽

Optimal Value ◽

Evolutionarily Stable

We consider a game-theoretical solution for an optimal stopping problem which we describe in terms of a job-search problem with an infinite population of candidates and an infinite population of posts of varying value. Each candidate finds posts from the post population at unit rate. If a post found is still vacant, a candidate can either accept it or reject it. The reward to a candidate is the value of the post if one is accepted and zero if he never accepts a post. There are no costs for searching, no discounting of future rewards and no recall of previously found posts. The only pressure on a candidate to accept a post comes from the changing rate at which he finds vacant posts (and the values associated with them) as a result of the actions of the other candidates. It is not possible to define optimality for a single candidate without reference to the policies followed by the other candidates. We say a policy π is an evolutionarily stable strategy (ESS) if it has the following property: if all candidates used π and an individual candidate was given the option of changing his policy, then it would not be to his advantage to do so. We first find the optimal value function and optimal policy for the case of a single candidate operating in an environment where the distribution of posts on offer and the chance of finding one both vary with time in a known way. We then show that for the infinite population there is a unique ESS given by a control-limit policy π c, where the control-limit function c is the solution of a given differential equation with a given initial condition. This function c also gives the expected future reward function for any single candidate when all candidates use π c.

Download Full-text

Expressiveness and Nash Equilibrium in Iterated Boolean Games

ACM Transactions on Computational Logic ◽

10.1145/3439900 ◽

2021 ◽

Vol 22 (2) ◽

pp. 1-38

Author(s):

Julian Gutierrez ◽

Paul Harrenstein ◽

Giuseppe Perelli ◽

Michael Wooldridge

Keyword(s):

Nash Equilibrium ◽

Nash Equilibria ◽

Infinite Sequence ◽

Multi Agent Systems ◽

Temporal Logics ◽

Agent Systems ◽

Temporal Properties ◽

Multi Agent ◽

Game Theoretic ◽

Boolean Games

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent has a goal , represented using (a fragment of) Linear Temporal Logic ( ) . The goal captures agent ’s preferences, in the sense that the models of represent system behaviours that would satisfy . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

Download Full-text

Interval-Valued Intuitionistic Fuzzy Confidence Intervals

Journal of Intelligent Systems ◽

10.1515/jisys-2017-0139 ◽

2019 ◽

Vol 28 (2) ◽

pp. 307-319 ◽

Cited By ~ 1

Author(s):

Cengiz Kahraman ◽

Basar Oztaysi ◽

Sezi Cevik Onar

Keyword(s):

Decision Making ◽

Confidence Intervals ◽

Statistical Decision ◽

Infinite Population ◽

Intuitionistic Fuzzy ◽

Population Sizes ◽

Statistical Decision Making ◽

Vague Data ◽

Two Populations ◽

Interval Valued

Abstract Confidence intervals are useful tools for statistical decision-making purposes. In case of incomplete and vague data, fuzzy confidence intervals can be used for decision making under uncertainty. In this paper, we develop interval-valued intuitionistic fuzzy (IVIF) confidence intervals for population mean, population proportion, differences in means of two populations, and differences in proportions of two populations. The developed IVIF intervals can be used in cases of both finite and infinite population sizes. The developed fuzzy confidence intervals are equivalent decision-making tools to fuzzy hypothesis tests. We apply the proposed confidence intervals to the differences in the mean lives and failure proportions of two types of radiators used in automobiles, and a sensitivity analysis is given to check the robustness of the decisions.

Download Full-text

Revealed Preference Implications of Backward Induction and Subgame Perfection

American Economic Journal Microeconomics ◽

10.1257/mic.20180077 ◽

2020 ◽

Vol 12 (2) ◽

pp. 230-256

Author(s):

Pablo Schenone

Keyword(s):

Nash Equilibrium ◽

Decision Maker ◽

Revealed Preference ◽

Backward Induction ◽

Multiplayer Games ◽

Subgame Perfect Nash Equilibrium ◽

Subgame Perfection ◽

Choice Correspondence ◽

Necessary And Sufficient ◽

Weak Axiom

Consider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73)

Download Full-text