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

1993 ◽  
Vol 25 (2) ◽  
pp. 314-333 ◽  
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.

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

1993 ◽  
Vol 25 (02) ◽  
pp. 314-333 ◽  
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.

A LARGE POPULATION, GAME THEORETIC MODEL OF JOB-SEARCH WITH DISCOUNTING

2009 ◽  
Vol 11 (03) ◽  
pp. 301-320
Author(s):  
DAVID M. RAMSEY
Keyword(s):  
Job Search ◽  
Evolutionarily Stable Strategy ◽  
Large Population ◽  
Iterative Algorithms ◽  
Theoretic Model ◽  
Search Problem ◽  
Game Theoretic ◽  
Population Game ◽  
Game Theoretic Model ◽  
Evolutionarily Stable

This paper considers a large population, game theoretic job-search problem, in which the ratio of job searchers to jobs is α. There are n distinct types of jobs, each with an associated value. Each searcher can only accept one job and cannot recall a job previously rejected. Once a searcher accepts a job, no other searcher can obtain that particular job. The reward to a searcher is taken to be the value of the job he/she obtains discounted by a factor of e-γt, where t is the time spent searching and γ > 0. It is shown that a unique evolutionarily stable strategy (ESS) exists for such problems. Two iterative algorithms for approximating the ESS are considered. In the case where there are only two types of job, the ESS can be calculated directly.

The job search problem as an employer–candidate game

1990 ◽  
Vol 27 (04) ◽  
pp. 815-827 ◽  
Author(s):  
J. M. Mcnamara ◽  
E. J. Collins
Keyword(s):  
Nash Equilibrium ◽  
Decision Maker ◽  
Job Search ◽  
Infinite Sequence ◽  
Search Problem ◽  
Infinite Population ◽  
Countable Sequence ◽  
Unique Pair ◽  
Two Populations

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.

The job search problem as an employer–candidate game

1990 ◽  
Vol 27 (4) ◽  
pp. 815-827 ◽  
Author(s):  
J. M. Mcnamara ◽  
E. J. Collins
Keyword(s):  
Nash Equilibrium ◽  
Decision Maker ◽  
Job Search ◽  
Infinite Sequence ◽  
Search Problem ◽  
Infinite Population ◽  
Countable Sequence ◽  
Unique Pair ◽  
Two Populations

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.

scholarly journals Instability of cooperation in finite populations

2019 ◽  
Author(s):  
Chai Molina ◽  
David J. D. Earn
Keyword(s):  
Finite Population ◽  
Selection Process ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Evolution Of Cooperation ◽  
Implicit Assumption ◽  
Stable Strategy ◽  
Infinite Population ◽  
Snowdrift Game ◽  
Evolutionarily Stable

AbstractEvolutionary game theory has been developed primarily under the implicit assumption of an infinite population. We rigorously analyze a standard model for the evolution of cooperation (the multi-player snowdrift game) and show that in many situations in which there is a cooperative evolutionarily stable strategy (ESS) if the population is infinite, there is no cooperative ESS if the population is finite (no matter how large). In these cases, contributing nothing is a globally convergently stable finite-population ESS, implying that apparent evolution of cooperation in such games is an artifact of the infinite population approximation. The key issue is that if the size of groups that play the game exceeds a critical proportion of the population then the infinite-population approximation predicts the wrong evolutionary outcome (in addition, the critical proportion itself depends on the population size). Our results are robust to the underlying selection process.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

A dynamic programming approach to evolutionarily stable strategy theory

1980 ◽  
Vol 12 (1) ◽  
pp. 3-5 ◽  
Author(s):  
C. Cannings ◽  
D. Gardiner
Keyword(s):  
Dynamic Programming ◽  
Density Function ◽  
Evolutionarily Stable Strategy ◽  
Programming Approach ◽  
Stable Strategy ◽  
War Of Attrition ◽  
Dynamic Programming Approach ◽  
The Individual ◽  
Image Position ◽  
Evolutionarily Stable

In the war of attrition (wa), introduced by Maynard Smith (1974), two contestants play values from [0, ∞), the individual playing the longer value winning a fixed prize V, and both incurring a loss equal to the lesser of the two values. Thus the payoff, E(x, y) to an animal playing x against one playing y, is A more general form (Bishop and Cannings (1978)) has and it was demonstrated that with and there exists a unique evolutionarily stable strategy (ess), which is to choose a random value from a specified density function on [0, ∞). Results were also obtained for strategy spaces [0, s] and [0, s).

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