中国现行财政体制下“买税”行为的博弈分析

博弈论为理论依据,通过对高、低两种任务下买税利益团体和上级监管部门的利益偏好和行为特征进行建模对比分析,考察影响其行为的各种因素,从经济学角度探求引起“买税”行为的根源,并试着给出建议.     

Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions

In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity and general increasing condition on y, with Lipschitz condition on z.     

Explicit optimal value for Dynkin's stopping game

Under the One-step Look Ahead rule of Dynamic Programming, an explicit game value of Dynkin's stopping problem for a Markov chain is obtained by using a potential operator. The condition on the One-step rule could be extended to the k-step and infinity-step rule. We shall also decompose the game value as the sum of two explicit functions under these rules.     

Evolution towards the Maximum Clique

As is well known, the problem of finding a maximum clique in a graph isNP-hard. Nevertheless, NP-hard problems may have easy instances. This paperproposes a new, global optimization algorithm which tries to exploit favourabledata constellations, focussing on the continuous problem formulation: maximizea quadratic form over the standard simplex. Some general connections of thelatter problem with dynamic principles of evolutionary game theory areestablished. As an immediate consequence, one obtains a procedure whichconsists (a) of an iterative part similar to interior-path methods based on theso-called replicator dynamics; and (b) a routine to escape from inefficient,locally optimal solutions. For the special case of finding a maximum clique ina graph where the quadratic form arises from a regularization of the adjacencematrix, part (b), i.e. escaping from maximal cliques not of maximal size, isaccomplished with block pivoting methods based on (large) independent sets,i.e. cliques of the complementary graph. A simulation study is included whichindicates that the resulting procedure indeed has some merits.     

On the strategic origin of Brownian motion in finance

This paper is concerned with the strategic use of a private information on the stock market. A repeated auction model is used to analyze the evolution of the price system on a market with asymmetric information.  The model turns out to be a zero-sum repeated game with one-sided information, as introduced by Aumann and Maschler.  The stochastic evolution of the price system can be explicitly computed in the n times repeated case. As n grows to ∞, this process tends to a continuous time martingale related to a Brownian Motion.  This paper provides in this way an endogenous justification for the appearance of Brownian Motion in Finance theory. Received: February 2002     

Nash equilibria in random games

We consider Nash equilibria in 2‐player random games and analyze a simple Las Vegas algorithm for finding an equilibrium. The algorithm is combinatorial and always finds a Nash equilibrium; on m × n payoff matrices, it runs in time O(m²nloglog n + n²mloglog m) with high probability. Our result follows from showing that a 2‐player random game has a Nash equilibrium with supports of size two with high probability, at least 1 − O(1/log n). Our main tool is a polytope formulation of equilibria. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

A <Emphasis Type="Italic">d</Emphasis>-person Differential Game with State Space Constraints

We consider a network of d companies (insurance companies, for example) operating under a treaty to diversify risk. Internal and external borrowing are allowed to avert ruin of any member of the network. The amount borrowed to prevent ruin is viewed upon as control. Repayment of these loans entails a control cost in addition to the usual costs. Each company tries to minimize its repayment liability. This leads to a d -person differential game with state space constraints. If the companies are also in possible competition a Nash equilibrium is sought. Otherwise a utopian equilibrium is more appropriate. The corresponding systems of HJB equations and boundary conditions are derived. In the case of Nash equilibrium, the Hamiltonian can be discontinuous; there are d interlinked control problems with state constraints; each value function is a constrained viscosity solution to the appropriate discontinuous HJB equation. Uniqueness does not hold in general in this case. In the case of utopian equilibrium, each value function turns out to be the unique constrained viscosity solution to the appropriate HJB equation. Connection with Skorokhod problem is briefly discussed.     

Zero-sum differential games involving impulse controls

In this paper we are concerned with zero-sum differential games with impulse controls, as well as continuous and switching controls. The motivation is optimal impulse control problems with disturbances. The main result is the existence of the value function of the game. Our approach is the theory of viscosity solutions for Hamilton-Jacobi equations.Part of this paper was done while the author was a visiting scholar at INRIA, Sophia-Antipolis, France. This work was also partially supported by the Chinese NSF, the Chinese State Education Commission Science Foundation, and the Fok Ying Tung Education Foundation.     

Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network

We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperators and sustainable cooperation. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Newman-Watts small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. That is, frequency of cooperators peaks at a certain specific value of degree heterogeneity — neither the most heterogeneous case nor the most homogeneous one would favor the cooperators. Besides, the average degree of networks and the adopted update rule also affect the cooperation level.     

Repeated Downsian electoral competition

We analyze an infinitely repeated version of the Downsian model of elections. The folk theorem suggests that a wide range of policy paths can be supported by subgame perfect equilibria when parties and voters are sufficiently patient. We go beyond this result by imposing several suitable refinements and by giving separate weak conditions on the patience of voters and the patience of parties under which every policy path can be supported. On the other hand, we show that only majority undominated policy paths can be supported in equilibrium for arbitrarily low voter discount factors: if the core is empty, the generic case in multiple dimensions, then voter impatience leads us back to the problem of non-existence of equilibrium. We extend this result to give conditions under which core equivalence holds for a non-trivial range of voter and party discount factors, providing a game-theoretic version of the Median Voter Theorem in a model of repeated Downsian elections. J. Duggan was supported by the National Science Foundation, grant number 0213738, is gratefully acknowledged.