Divide-the-Dollar game revisited

In the Divide-the-Dollar (DD) game, two players simultaneously make demands to divide a dollar. Each player receives his demand if the sum of the demands does not exceed one, a payoff of zero otherwise. Note that, in the latter case, both parties are punished severely. A major setback of DD is that each division of the dollar is a Nash equilibrium outcome. Observe that, when the sum of the two demands x and y exceeds one, it is as if Player 1's demand x (or his offer (1−x) to Player 2) suggests that Player 2 agrees to λx < 1 times his demand y so that Player 1's demand and Player 2's modified demand add up to exactly one; similarly, Player 2's demand y (or his offer (1−y) to Player 1) suggests that Player 1 agrees to λyx so that λyx+y = 1. Considering this fact, we change DD's payoff assignment rule when the sum of the demands exceeds one; here in this case, each player's payoff becomes his demand times his λ; i.e., each player has to make the sacrifice that he asks his opponent to make. We show that this modified version of DD has an iterated strict dominant strategy equilibrium in which each player makes the egalitarian demand 1/2. We also provide a natural N-person generalization of this procedure.

Contests with the probability of a draw : a stochastic foundation

This article proposes a stochastic foundation for the contest success function (CSF for short) with a richer structure on the set of possible outcomes of the contest. Specifically, the analysis allows for the possibility of a draw, so that no contestant can claim a victory over all other players. Under plausible conditions, this article not only discovers new functional forms of CSFs, but also shows the newly derived CSFs have very different properties in equilibrium to those of conventional CSFs. For example, in contrast to the CSFs discussed in the contest literature, which always generate a unique pure strategy Nash equilibrium, the newly discovered CSFs admit the possibility of multiple equilibria.

Hotelling-downs competition with free entry when voters have an option to contest

Osborne shows that for almost all distributions of voters' preferences, a pure strategy Nash equilibrium does not exist in the classical Hotelling-Downs model of electoral competition with free entry. We show that equilibrium is generically possible if in addition one allows voters an option to announce their candidacy to compete side-by-side with office-seeking players. The model studied in this paper renders Osborne and the celebrated citizen-candidate model à la Osborne and Slivinski as two extreme cases. We characterize the equilibrium set with two central questions: (i) can there be equilibria where only voters contest? and (ii) are equilibria with contesting office-seeking players possible? We also show that in our general setting, extremists are typically voter-candidates so that in every two-party contest, office-seeking politicians stay out of competition.

A location game on disjoint circles

Two players are endowed with resources for setting up N locations on K identical circles, with N > K < 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. They face a resource mobility constraint such that not all N locations can be placed in the first round. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that for K = 1, the second mover always has a winning strategy in this game. In this paper we show that with K > 1, the second mover advantage disappears as in this case both players have a tying strategy. We also study a natural variant of this game where the resource mobility constraint is more stringent so that in each round each player chooses a single location where we show that the second mover advantage re-appears. We suggest some Nash equilibrium configurations of locations in both versions of the game.

A game-theoretic resource allocation approach for intercell device-to-device communications in cellular networks

Device-to-Device (D2D) communication is a recently emerged disruptive technology for enhancing the performance of current cellular systems. To successfully implement D2D communications underlaying cellular networks, resource allocation to D2D links is a critical issue, which is far from trivial due to the mutual interference between D2D users and cellular users. Most of the existing resource allocation research for D2D communications has primarily focused on the intracell scenario while leaving the intercell settings not considered. In this paper, we investigate the resource allocation issue for intercell scenarios where a D2D link is located in the overlapping area of two neighboring cells. Specifically, We present three intercell D2D scenarios regarding the resource allocation problem. To address the problem, we develop a repeated game model under these scenarios. Distinct from existing works, we characterize the communication infrastructure, namely Base Stations (BSs), as players competing resource allocation quota from D2D demand, and we define the utility of each player as the payoff from both cellular and D2D communications using radio resources. We also propose a resource allocation algorithm and protocol based on the Nash equilibrium derivations. Numerical results indicate that the developed model not only significantly enhances the system performance including sum rate and sum rate gain, but also sheds lights on resource configurations for intercell D2D scenarios.

Nash Demand Game and the Kalai-Smorodinsky Solution

We introduce two new variations on the Nash demand game. One, like all known Nash-like demand games so far, has the Nash solution outcome as its equilibrium outcome. In the other, the range of solutions depends on an exogenous breakdown probability; surprisingly, the Kalai-Smorodinsky outcome proves to be the most robust equilibrium outcome. While the Kalai- Smorodinsky solution always finishes on top, there is no possible general ranking among the remaining solution concepts considered; in fact, the rest of the solution concepts take their turns at the bottom at various bargaining problems, depending on the specifics of the bargaining setup.

The effects of facilitation on punctuated equilibrium in e-collaboration projects

Information technology has transformed the “heartland” of education around the world. Classrooms are global, students international, but traditional methods and their adjacent challenges persist or are exacerbated in online schoolhouses. There is reason to believe that team performance of online students completing team projects can be significantly improved by the active participation of a facilitator. What could explain such improvement? Given the communication barriers that learners can experience using e-learning technologies, the skill of a teacher at facilitating an understanding of e-collaboration and the prescient need to facilitate collaborative skills at all times is essential to a successful educational result. There may also be generational learning style issues to consider. One practical, proven tool is progress reporting. This paper reviews the literature and reflects on author experiences in the online education of Management students at universities in the United States and Australia to draw theoretical connections with communication, leadership, and punctuated equilibrium relevant to contemporary educational practice. The implications of effective facilitation of student teams for Management education and management of student performance are explored.

Hunting the unobservables for optimal social security a general equilibrium approach

We study the optimal size of a pay-as-you-go social security program for an economy composed of both permanent-income and hand-to-mouth consumers. While previous work on this topic is framed within a two-period partial equilibrium setup, we study this issue in a life-cycle general equilibrium model. Because this type of welfare analysis depends critically on unobservable preference parameters, we methodically consider all parameterizations of the unobservables that are both feasible and reasonable—all parameterizations that can mimic key features of macro data (feasible) while still being consistent with micro evidence and convention (reasonable). The baseline model predicts that the optimal tax rate is between 6 percent and 15 percent of wage income.

The equilibrium relations between stock index and bond index: evidence from Bursa Malaysia

This paper aims at examining the correlation structure, co-integration relationship and volatility linkage between stock and bond market indices over a period from January 1994 to June 2004. This study uses Johansen Cointegratoin test, VECM-X model and GARCH (1,1) with MDH model to examine the existence of long-term relation and volatility linkage between stock and bond market. The findings shed some light on the existence of mean-reverting pattern of correlation across different economic environments.  Findings on co-movement of stock and bond indices suggest an equilibrium relationship with short-term error correction. While evidence from volatility linkage also suggests that bond market cannot provide a meaningful explanation for conditional volatility in stock market, therefore, rejecting the mixture of distribution hypothesis.

Doubling fish exports or garment exports : which would benefit the Fijian economy most? Evidence from a computable general equilibrium model

The need to diversify Fiji's export base has been identified as an important avenue for reducing Fiji's vulnerabilities in international trade. This paper poses the question: Doubling fish exports or garment exports: which would be most beneficial for the Fijian economy? To achieve the goal of this paper, the computable general equilibrium model is used, this being at the forefront of research on 'impact studies'. The main finding is that when garment exports and fish exports are doubled, the benefits to the Fijian economy are greater from garment exports, suggesting that the latter has stronger linkages with the rest of the economy. On the basis of this finding, policymakers should divert resources towards sustaining the garment industry whose future is uncertain due to expiring trade agreements and unstable economic policies.

Using graphics calculators and spreadsheets in chemistry : solving equilibrium problems

Discusses tabular and graphical approaches to equilibrium calculations.

The nash solution and relevant expansions

In this paper we propose a new axiom, Relevant Balanced Expansion Monotonicity (RBEM), to replace Nash’s original Independence of Irrelevant Alternatives (HA) axiom. Using the RBEM axiom and the other three original axioms suggested by Nash we provide a characterization of the Nash Solution.

A simple two-axiom characterization of the Nash solution

The oldest and best-known cooperative bargaining solution concept is the Nash solution. Nash [2] characterized his seminal solution concept by using the axioms of ‘Independence of Irrelevant Alternatives’ (IIA), ‘Weak Pareto Optimality’ (WPO), ‘Symmetry’ (SYM), and ‘Scale Invariance’ (SI). Except for WPO, these axioms have been at the center of controversy (especially the most crucial axiom, IIA). This paper considers a new and simple axiom ‘Focal Relevance of a Pareto-optimal Midpoint’ (FRPM). It turns out that the Nash solution can be characterized by WPO and FRPM only.