scholarly journals Two-person red-and-black games with bet-dependent win probability functions

2006 ◽  
Vol 43 (04) ◽  
pp. 905-915 ◽  
Author(s):  
May-Ru Chen ◽  
Shoou-Ren Hsiau
Keyword(s):  
Nash Equilibrium ◽  
Sufficient Condition ◽  
Probability Functions ◽  
Game Player ◽  
Unique Nash Equilibrium

In this paper a two-person red-and-black game is investigated. We suppose that, at every stage of the game, player I's win probability, f, is a function of the ratio of his bet to the sum of both players' bets. Two results are given: (i) if f is convex then a bold strategy is optimal for player I when player II plays timidly; and (ii) if f satisfies f(s)f(t) ≤ f(st) then a timid strategy is optimal for player II when player I plays boldly. These two results extend two formulations of red-and-black games proposed by Pontiggia (2005), and also provide a sufficient condition to ensure that the profile (bold, timid) is the unique Nash equilibrium for players I and II. Finally, we give a counterexample to Pontiggia's conjecture about a proportional N-person red-and-black game.

scholarly journals Two-person red-and-black games with bet-dependent win probability functions

2006 ◽  
Vol 43 (4) ◽  
pp. 905-915 ◽  
Author(s):  
May-Ru Chen ◽  
Shoou-Ren Hsiau
Keyword(s):  
Nash Equilibrium ◽  
Sufficient Condition ◽  
Probability Functions ◽  
Game Player ◽  
Unique Nash Equilibrium

In this paper a two-person red-and-black game is investigated. We suppose that, at every stage of the game, player I's win probability, f, is a function of the ratio of his bet to the sum of both players' bets. Two results are given: (i) if f is convex then a bold strategy is optimal for player I when player II plays timidly; and (ii) if f satisfies f(s)f(t) ≤ f(st) then a timid strategy is optimal for player II when player I plays boldly. These two results extend two formulations of red-and-black games proposed by Pontiggia (2005), and also provide a sufficient condition to ensure that the profile (bold, timid) is the unique Nash equilibrium for players I and II. Finally, we give a counterexample to Pontiggia's conjecture about a proportional N-person red-and-black game.

scholarly journals Economic Analysis of Accident Law: A New Liability Rule that Induces Socially Optimal Behaviour in Case of Limited Information

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Astha Srivastava ◽  
Ankur Srivastava
Keyword(s):  
Nash Equilibrium ◽  
Economic Analysis ◽  
Standard Of Care ◽  
Limited Information ◽  
Liability Rule ◽  
Rule Based ◽  
Liability Rules ◽  
Levels Of Care ◽  
Unique Nash Equilibrium ◽  
Optimal Behaviour

AbstractIn accident law, we seek a liability rule that will induce both the parties to adopt socially optimal levels of precaution. Economic analysis, however, shows that none of the commonly used liability rules induce both parties to adopt optimal levels, if courts have access only to ‘Limited Information’ on. In such a case, it has also been established (K. (2006). Efficiency of liability rules: a reconsideration. J. Int. Trade Econ. Dev. 15: 359–373) that no liability rule based on cost justified untaken precaution as a standard of care can be efficient. In this paper, we describe a two-step liability rule: the rule of negligence with the defence of relative negligence. We prove that this rule has a unique Nash equilibrium at socially optimal levels of care for the non-cooperative game, and therefore induces both parties to adopt socially optimal behaviour even in case of limited information.

scholarly journals Efficiency and Equilibrium in Network Games: An Experiment

2021 ◽  
pp. 1-44
Author(s):  
Edoardo Gallo ◽  
Chang Yan
Keyword(s):  
Nash Equilibrium ◽  
Network Structure ◽  
Economic Systems ◽  
Central Feature ◽  
Network Games ◽  
Trade Off ◽  
Network Game ◽  
Asymmetric Networks ◽  
Unique Nash Equilibrium

Abstract The tension between efficiency and equilibrium is a central feature of economic systems. We examine this trade-off in a network game with a unique Nash equilibrium in which agents can achieve a higher payoff by following a “collaborative norm”. Subjects establish and maintain a collaborative norm in the circle, but the norm weakens with the introduction of one hub connected to everyone in the wheel. In complex and asymmetric networks of 15 and 21 nodes, the norm disappears and subjects’ play converges to Nash. We provide evidence that subjects base their decisions on their degree, rather than the overall network structure.

Applications to Economics

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Nash Equilibrium ◽  
Private Information ◽  
Price Competition ◽  
Quantal Response ◽  
Unique Nash Equilibrium ◽  
Common Effort ◽  
The Cost ◽  
All Pay Auction ◽  
Individual Effort ◽  
Applications To Economics

This chapter explores whether the equilibrium effects of noisy behavior can cause large deviations from standard predictions in economically relevant situations. It considers a simple price-competition game, which is also partly motivated by the possibility of changing a payoff parameter that has no effect on the unique Nash equilibrium, but which may be expected to affect quantal response equilibrium. In the minimum-effort coordination game studied, any common effort in the range of feasible effort levels is a Nash equilibrium, but one would expect that an increase in the cost of individual effort or an increase in the number of players who are trying to coordinate would reduce the effort levels observed in an experiment. The chapter presents an analysis of the logit equilibrium and rent dissipation for a rent-seeking contest that is modeled as an “all-pay auction.” The final two applications in this chapter deal with auctions with private information.

scholarly journals Qualitative criterion for interception in a pursuit/evasion game

2009 ◽  
Vol 466 (2117) ◽  
pp. 1365-1371 ◽  
Author(s):  
J. A. Morgan
Keyword(s):  
Nash Equilibrium ◽  
Initial Position ◽  
Initial Time ◽  
Sufficient Condition ◽  
Pursuit Evasion ◽  
Evasion Game ◽  
Differential Pursuit ◽  
The Future ◽  
Qualitative Criterion ◽  
Future Cone

A qualitative account is given of a differential pursuit/evasion game. A criterion for the existence of an intercept solution is obtained using future cones that contain all attainable trajectories of target or interceptor originating from an initial position. A sufficient and necessary conditon that an opportunity to intercept always exists is that, after some initial time, the future cone of the target be contained within the future cone of the interceptor. The sufficient condition may be regarded as a kind of Nash equilibrium.

scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (04) ◽  
pp. 1165-1172
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

Sign in / Sign up

Export Citation Format

Share Document