David M. Ramsey

A large population job search game with discrete time

Abstract A job search problem is considered, in which there is a large population of jobs initially available and a large population of searchers. The ratio of the number of searchers to the number of jobs is α . Each job has an associated value from a known distribution. At each of N moments the searchers observe a job, whose value comes from the distribution of the values of currently available jobs. If a searcher accepts a job, s/he ceases searching and the job becomes unavailable. Hence, the distribution of the values of available jobs changes over time. Also, the ratio of the number of those still searching to the number of available jobs changes. The model is presented and Nash equilibrium strategies for such problems are considered. By definition, when all the population use a Nash equilibrium strategy, the optimal response of an individual is to use the same strategy. Conditions are given that ensure the existence of a unique Nash equilibrium strategy. Examples are given to illustrate the model and present different approaches to solving such problems.

Selection of a correlated equilibrium in Markov stopping games

Abstract This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players’ decisions according to some optimality criterion. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the best choice problem are given. Several concepts of criteria for selecting a correlated equilibrium are used.

On a Simple Game Theoretical Equivalence of Voting Majority Games with Vetoes of First and Second Degrees

Introducing a veto into the process of group decision making (voting, aggregating preferences) drastically changes the position of decision makers and, consequently, it changes their power index. In this paper we derive the Shapley-Shubik and Penrose-Banzhaf indices for a class of voting games with vetoes. We also present a way of constructing a simple voting game which is equivalent to a game with vetoes of first degree. This simplifies the calculation of power indices by allowing us to use standard algorithms which are available online.

Bilateral Approach to the Secretary Problem

A mathematical model of competitive selection of the applicants for a post is considered. There are N applicants of similar qualifications on an interview list. The applicants come in a random order and their salary demands are distinct. Two managers, I and II, will interview them one at a time. The aim of the manager is to obtain the applicant which demands minimal salary. The candidate can be accepted only at the moment of its appearance. When both manager want to accept the same candidate, then some rule of assignment to one of the manager is applied. Any candidate hired by the manager will accept the offer with some given probability. An candidate can be hired only at the moment of its appearance. At each moment n one candidate is presented. The considered problem is a generalisation of the best choice problem with uncertain employment and the game version of it with priority or random priority. The general stopping game model is constructed. The algorithms of construction of the game value and the equilibrium strategies are given. An example is solved.

A Dynamic Model of a Decision Making Body Where the Power of Veto Can Be Invoked

Classical analysis of the power of individuals or groups in decision making bodies tends to consider processes of coalition formation in isolation from each other. However, the results of attempts to form a winning coalition will affect the dynamics of coalition formation in the future, particularly when certain players are endowed with the power of veto. When a voter invokes their power of veto to block a generally popular motion, this is likely to provoke retaliation from the supporters of the motion. For this reason, even if a player is not in favor of a bill and can block it, it may be favorable for that party to abstain rather than veto in return for support regarding issues to be considered in the future. Hence, players should only use their power of veto if they are very strongly against a bill. In this paper, we present a model of voting in which the results of previous votes can affect the process of coalition formation. We present a model of such a dynamic voting game and present the form of an equilibrium in such a game. This theory is illustrated using an example based on the voting procedures used in the United Nations Security Council.

An Equilibrium in a Sequence of Decisions with Veto of First Degree

In this paper we model a sequence of decisions via a simple majority voting game with some players possessing an unconditional or conditional veto. The players vote (yes, no or abstain) on each motion in an infinite sequence, where two rounds of voting take place on each motion. The form of an equilibrium with retaliation is introduced, together with necessary and sufficient conditions for an equilibrium in such a game. A theorem about the form of the equilibrium is proved: given that one veto player abstained in the first round, in the second round of voting on a motion: (1) a veto player should vote for the motion if the value of the j-th motion to the i-th player (measured relative to the status quo) is greater than t 2 , veto if it is less than t 1 and otherwise abstain; (2) a non-veto player should vote for the motion if the value of the j-th motion to the i-th player (measured relative to the status quo) is greater than t 3 and otherwise abstain; (3) the thresholds t 1 , t 2 and t 3 satisfy given conditions.

Norms of Egality and the Gap between Attitudes and Behaviour amongst Polish Students: An Experimental Study

DOI: 10.14254/2071789X.2017/10-3/16 ABSTRACT. Social norms and ideals play an important role in determining the attitudes and behaviour of individuals. However, in many scenarios adhering to such norms or ideals leads to an individual incurring costs. In such a case, a gap may appear between the attitudes (intentions) and the behaviour of an individual. This article considers the gap between declared and observed readiness to punish an individual seen to act unfairly on the basis an experimental version of the Ultimatum Game. The authors highlight the difficulties of analysing such a gap. This experimental game was played by a sample of 1540 Polish students of state universities in each of the 16 Polish regions. These participants also filled out a questionnaire regarding their social capital, as well as attitudes and beliefs related to inequality and reciprocation. An analysis of the behaviour of individuals is presented, together with a mathematical model describing the gap between behaviour and stated intentions.

A Large Population Parental Care Game with Asynchronous Moves

This article considers two game-theoretic models of parental care which take into account the feedback between patterns of care and the operational sex ratio. Attention is paid to fish species which care for their young by mouthbrooding, in particular to St. Peter’s Fish. It is assumed here that individuals can be in one of the two states: searching for a mate or breeding (including caring for their offspring). However, the sets of states can be adapted to the physiology of a particular species. The length of time an individual remains in the breeding state depends on the level of care he/she gives. According to one model, parents make their decision regarding the amount of care they give simultaneously. Under the second model, one individual in a pair (for convenience, the female) makes her decision before the male makes his decision. When in the searching state, individuals find partners at a rate dependent on the proportion of members of the opposite sex searching. These rates are defined to satisfy the Fisher condition that the total number of offspring of males equals the total number of offspring of females. The operational sex ratio is not defined exogenously, but can be derived from the adult sex ratio and the pattern of parental care. The results obtained go some way to explain the variety of parental care behaviour observed in fish, in particular the high frequency of male care, although further work is required to explain the exact patterns observed.