Tax Competition between Symmetric Countries for Large Asymmetric Investors

In a dynamic two-period game between two symmetric countries, we show that a unique subgame-perfect equilibrium arises during the initial stage of the game. A mixed taxation regime arises in the equilibrium where one country adopts a non-preferential taxation regime while its competitor adopts a preferential taxation regime. The country with a non-preferential taxation regime earns a higher tax revenue compared to the country with a preferential taxation regime. A tax holiday does not arise during the initial stage of the game when the size of the mobile capital base that enters during the later stage is considerably larger than the size of the mobile capital base that enters the economy during the initial stage. We provide the complete characterization and proof of the uniqueness of the mixed strategy Nash equilibrium.JEL classification: F21, H21, H25, H87

Dynamic Tax Competition, Home Bias and the gain from Non-preferential Taxation Regimes: A case for unilateral commitment

A country has an incentive to unilaterally commit to a non-preferential taxation regime even though the competitor adopts a preferential taxation regime. We show that a mixed taxation regime arises in a dynamic two-period model of tax competition between two symmetric countries where an investor has home-bias for the country where he/she invests in the initial period. A scenario where competing countries jointly adopt non-preferential taxation regimes is also a subgame-perfect equilibrium. The tax revenue of the country which adopts a preferential taxation regime in a mixed taxation regime is equal to the tax revenue a country receives when competing countries jointly adopt a non-preferential taxation regime.JEL classification: F21; H21; H25; H87

Voting behavior under outside pressure: promoting true majorities with sequential voting?

When including outside pressure on voters as individual costs, sequential voting (as in roll call votes) is theoretically preferable to simultaneous voting (as in recorded ballots). Under complete information, sequential voting has a unique subgame perfect equilibrium with a simple equilibrium strategy guaranteeing true majority results. Simultaneous voting suffers from a plethora of equilibria, often contradicting true majorities. Experimental results, however, show severe deviations from the equilibrium strategy in sequential voting with not significantly more true majority results than in simultaneous voting. Social considerations under sequential voting—based on emotional reactions toward the behaviors of the previous players—seem to distort subgame perfect equilibria.

Conditional loyalty and its implications for pricing

Bertrand–Edgeworth competition has recently been analyzed under imperfect buyer mobility, as a game in which, once prices are chosen, a static buyer subgame (BS) is played where the buyers choose which seller to visit (see, e.g., Burdett et al. in J Political Econ 109:1060–1085, 2001). Our paper considers a symmetric duopoly where two buyers play a two-stage BS of imperfect information after price setting. An “assessment equilibrium” of the BS is shown to exist in which, with prices at the two firms sufficiently close to each other, the buyers keep loyal if previously served. Conditional loyalty is proved to increase the duopolists’ market power: at the corresponding subgame perfect equilibrium of the entire game, the uniform price is higher than that corresponding to the equilibrium of the BS in which the buyers are persistently randomizing.

The equal collective gains value in cooperative games

The property of equal collective gains means that each player should obtain the same benefit from the cooperation of the other players in the game. We show that this property jointly with efficiency characterize a new solution, called the equal collective gains value (ECG-value). We introduce a new class of games, the average productivity games, for which the ECG-value is an imputation. For a better understanding of the new value, we also provide four alternative characterizations of it, and a negotiation model that supports it in subgame perfect equilibrium.

Atomic Dynamic Flow Games: Adaptive vs. Nonadaptive Agents

We propose a game model for selfish routing of atomic agents, who compete for use of a network to travel from their origins to a common destination as quickly as possible. We follow a frequently used rule that the latency an agent experiences on each edge is a constant transit time plus a variable waiting time in a queue. A key feature that differentiates our model from related ones is an edge-based tie-breaking rule for prioritizing agents in queueing when they reach an edge at the same time. We study both nonadaptive agents (each choosing a one-off origin–destination path simultaneously at the very beginning) and adaptive ones (each making an online decision at every nonterminal vertex they reach as to which next edge to take). On the one hand, we constructively prove that a (pure) Nash equilibrium (NE) always exists for nonadaptive agents and show that every NE is weakly Pareto optimal and globally first-in first-out. We present efficient algorithms for finding an NE and best responses of nonadaptive agents. On the other hand, we are among the first to consider adaptive atomic agents, for which we show that a subgame perfect equilibrium (SPE) always exists and that each NE outcome for nonadaptive agents is an SPE outcome for adaptive agents but not vice versa.

Costless delay in negotiations

We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

Synthesis of equilibria in infinite-duration

In this survey, we propose a comprehensive introduction to game theory applied to computer-aided synthesis. We study multi-player turn-based infinite-duration games played on a finite directed graph such that each player aims at maximizing a payoff function. We present the well-known notions of Nash equilibrium and subgame perfect equilibrium, as well as interesting strategy profiles of players as response to the strategy announced by a specific player. We provide classical and recent results about the related threshold synthesis problem.

Consistent Allocation of Emission Responsibility in Fossil Fuel Supply Chains

Since 2016, Canada’s federal government has pledged to factor in upstream emissions during the environmental impact assessment of fossil fuel energy projects. The upstream emissions attributable to a proposed project could be compared against a rejection threshold—a maximum permissible level of emissions—or the firm could be mandated to offset the attributed emissions. We adopt a cooperative game-theoretic model and propose the nucleolus mechanism to apportion upstream emission responsibilities in a fossil fuel supply chain, represented by a directed tree, wherein the nodes correspond to various entities in the supply chain such as extractors, distributors, refineries, and end consumers. The nucleolus allocation avoids the distortionary effects of double counting and exhibits a certain consistency property that is especially important in a regulatory context wherein fossil fuel supply chains span multiple legal jurisdictions. We develop a polynomial-time algorithm to compute the nucleolus and further prove that it arises as the unique subgame perfect equilibrium allocation of a noncooperative game induced by two easily stated and verifiable policies, thereby providing an implementation framework. We then demonstrate the strong Nash stability of the nucleolus mechanism subject to the two policies, study its sensitivity to parameter changes, and characterize it on the basis of fairness considerations. Furthermore, under the common assumption that the emissions allocated to a firm and the resulting financial penalties do not impact the revenues from the firm’s core operations, we also provide lower-bound guarantees on the welfare gains it delivers to firms in the fossil fuel supply chain and on the incentives it offers such firms to adopt emission abatement technologies. Finally, we contextualize our discussion with a case study on a proposed expansion of the Trans Mountain pipeline in Western Canada. This paper was accepted by Chung Piaw Teo, optimization.