DOES NOISE UNDERMINE THE FIRST-MOVER ADVANTAGE? AN EVOLUTIONARY ANALYSIS OF BAGWELL'S EXAMPLE

2000 ◽  
Vol 02 (01) ◽  
pp. 83-96 ◽  
Author(s):  
JÖRG OECHSSLER ◽  
KARL H. SCHLAG
Keyword(s):  
Mixed Strategy ◽  
Pure Strategy ◽  
Subgame Perfect Equilibrium ◽  
Evolutionary Analysis ◽  
Perfect Equilibrium ◽  
Learning Dynamics ◽  
Strategy Equilibrium ◽  
First Mover Advantage ◽  
Almost All ◽  
First Mover

Bagwell (1995) considered a simple Stackelberg-type game in which one player benefits from the other's ability to observe his move, assuming they play the unique subgame perfect equilibrium. He showed that introducing noise in the observability of the move eliminates that equilibrium, and thus the advantage. Van Damme and Hurkens (1997) objected that the noisy game also has a mixed strategy equilibrium close to the pure strategy one Bagwell had eliminated. However, we analyse the noisy game with a wide variety of evolutionary and learning dynamics, and find that almost all admit the no-first-mover-advantage equilibrium as a possible outcome, and often they select it uniquely.

The War against the Taliban

2015 ◽  
Vol 6 (3) ◽  
pp. 18-27 ◽  
Author(s):  
Lucía Martínez Ordóñez ◽  
Jörg Schimmelpfennig
Keyword(s):  
Information Asymmetry ◽  
Mixed Strategy ◽  
Operation Enduring Freedom ◽  
Irregular Warfare ◽  
Mixed Strategy Equilibrium ◽  
Strategy Equilibrium ◽  
First Mover Advantage ◽  
Rotary Wing ◽  
First Mover

Operation Enduring Freedom was hampered by a chronic shortage of attack helicopters available to ISAF forces in Afghanistan. Tactical operations into Taliban-held territory were launched even though close air support capable of dealing with “danger close” situations could not be assigned in advance. It led to significant ISAF casualties if the Taliban decided to fight back rather than withdraw. Departing from a Clausewitz-style, i.e. second-mover advantage, mixed-strategy equilibrium and taking account of the “Irregular Warfare” nature of the pay-offs, the paper looks into the existence of strategic moves. In particular, as playing a mixed strategy if rotary wing air support is unavailable merely incentivises a more aggressive Taliban response to any kind of operation due to the information asymmetry, it is argued that by moving away from the mixed-strategy equilibrium ISAF casualties in properly supported operations could be reduced, thus handing a first-mover advantage to ISAF.

scholarly journals Bundling and Competition for Slots

2012 ◽  
Vol 102 (5) ◽  
pp. 1957-1985 ◽  
Author(s):  
Doh-Shin Jeon ◽  
Domenico Menicucci
Keyword(s):  
Marginal Cost ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Policy Implications ◽  
Digital Goods ◽  
Efficient Technology ◽  
Pure Strategy Equilibrium ◽  
Clear Cut ◽  
Mixed Strategy Equilibrium ◽  
Strategy Equilibrium

We consider competition between sellers selling multiple distinct products to a buyer having k slots. Under independent pricing, a pure strategy equilibrium often does not exist, and equilibrium in mixed strategy is never efficient. When bundling is allowed, each seller has an incentive to bundle his products, and an efficient “technology-renting” equilibrium always exists. Furthermore, in the case of digital goods or when sales below marginal cost are banned, all equilibria are efficient. Comparing the mixed-strategy equilibrium with the technology-renting equilibrium reveals that bundling often increases the buyer's surplus. Finally, we derive clear-cut policy implications.(JEL D43, D86, K21, L13, L14, L41, L82)

On the Foundations of Nash Equilibrium

1996 ◽  
Vol 12 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Hans Jørgen Jacobsen
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Game Theory ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Mixed Strategies ◽  
Positive Theory ◽  
Equilibrium Concept ◽  
Strategy Equilibrium ◽  
Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

scholarly journals Simultaneous and sequential voting under general decision rules

2018 ◽  
Vol 30 (4) ◽  
pp. 477-488 ◽  
Author(s):  
Friedel Bolle
Keyword(s):  
Pure Strategy ◽  
Decision Rules ◽  
Subgame Perfect Equilibrium ◽  
Equal Weight ◽  
Perfect Equilibrium ◽  
Roll Call ◽  
General Rules ◽  
The Us ◽  
Sequential Voting ◽  
Us Senate

In an economic theory of voting, voters have positive or negative costs of voting in favor of a proposal and positive or negative benefits from an accepted proposal. When votes have equal weight then simultaneous voting mostly has a unique pure strategy Nash equilibrium which is independent of benefits. Voting with respect to (arbitrarily small) costs alone, however, often results in voting against the ‘true majority’ . If voting is sequential as in the roll call votes of the US Senate then, in the unique subgame perfect equilibrium, the ‘true majority’ prevails. It is shown that the result for sequential voting holds also with different weights of voters (shareholders), with multiple necessary majorities (European Union decision-making), or even more general rules. Simultaneous voting in the general model has more differentiated results.

A GAME OF SETTLEMENTS IN PUBLIC CONTRACTS

2009 ◽  
Vol 11 (02) ◽  
pp. 157-179
Author(s):  
WILFRIED PAUWELS ◽  
PETER M. KORT
Keyword(s):  
Mixed Strategy ◽  
Pure Strategy ◽  
Public Project ◽  
True Cost ◽  
Strategy Equilibrium ◽  
Proposal A ◽  
Pooling Equilibrium ◽  
The Government ◽  
The Cost ◽  
Separating Equilibrium

The paper considers a public authority wishing to carry out a major public project. As a result of competitive bidding the project is assigned to the firm with the lowest bid. The cost of the project is uncertain in the sense that it can be low or high. After the bidding process the firm observes the true cost, while the government remains uninformed. After learning about the true cost, the firm can start to renegotiate the contract by proposing an increase of the price. Such an increase is only justified in case costs are high. If the government rejects the new price proposal, a law suit follows. This situation is modeled as a signaling game. If the prior probability of the costs being low is low (high), a pooling (separating) equilibrium occurs. In the pooling equilibrium the government always accepts the firm's proposal. In the separating equilibrium the government can apply a mixed strategy when costs are high. Then it goes to court with a certain probability. Compared to a pure strategy, the mixed strategy has the advantage that legal costs are lower. In our economic analysis we compare the American and the English rule for sharing the litigation expenses. A main result is that under the American rule the legal expenses are lower and welfare is higher in the mixed strategy equilibrium. We also study the importance of the firm's commitment to its new price proposal.

Supplier Competition and Cost Reduction with Endogenous Information Asymmetry

2020 ◽  
Vol 22 (5) ◽  
pp. 996-1010
Author(s):  
Cuihong Li
Keyword(s):  
Supply Chain ◽  
Information Asymmetry ◽  
Cost Reduction ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Problem Definition ◽  
Optimal Size ◽  
Strategy Equilibrium ◽  
Endogenous Information ◽  
The Impact

Problem definition: We consider a buyer sourcing from multiple competing suppliers who exert cost-reduction efforts before procurement contracts are awarded. Academic/practical relevance: The supply chain is subject to the classic hold-up problem—as the lack of a contract commitment hinders suppliers’ incentives to make investment upfront—complicated with supplier competition. Methodology: With deterministic cost-reduction outcomes, suppliers will not exert any effort if this effort is observable, and a pure-strategy equilibrium does not exist if the effort is unobservable. We analyze the mixed-strategy equilibrium with unobservable supplier effort, in which suppliers randomize their efforts and the buyer designs an optimal procurement mechanism. Results: We show that the optimal procurement mechanism can be implemented by a conventional single-price reverse auction with a random reserve price. The mixed strategy of supplier effort generates endogenous information asymmetry on supplier costs that provides suppliers with information rent, which sustains their efforts. The endogenous information asymmetry improves effort efficiency (by inducing positive supplier effort), yet introduces trade inefficiency (by causing the possible failure of trade between the parties). Although increasing supplier competition (measured by the number of suppliers) hurts the effort efficiency, it improves trade efficiency. As a result, the buyer is always better off introducing supplier competition by including more than one supplier in the supply base. However, the desired supply base size (number of suppliers) depends on the product revenue: For high-margin goods, the optimal size is achieved with two suppliers, whereas for low-margin goods, a larger supply base is better for the buyer. We show that the result based on deterministic cost reduction can be established as a limit of the case when uncertainty in cost reduction exists and shrinks to null. Managerial implications: Our study helps to understand the impact of supplier competition when supply-chain parties deliberately make their actions unpredictable to avoid being held up. The findings provide managerial guidance on procurement auction and supply base designs.

FRACTAL GEOMETRY OF EQUILIBRIUM PAYOFFS IN DISCOUNTED SUPERGAMES

Fractals ◽  
2014 ◽  
Vol 22 (04) ◽  
pp. 1450016 ◽  
Author(s):  
KIMMO BERG ◽  
MITRI KITTI
Keyword(s):  
Hausdorff Dimension ◽  
Fractal Geometry ◽  
Pure Strategy ◽  
Subgame Perfect Equilibrium ◽  
Iterated Function Systems ◽  
Perfect Equilibrium ◽  
Iterated Function ◽  
Graph Presentation ◽  
Perfect Monitoring

This paper examines the pure-strategy subgame-perfect equilibrium payoffs in discounted supergames with perfect monitoring. It is shown that the equilibrium payoffs can be identified as sub-self-affine sets or graph-directed iterated function systems. We propose a method to estimate the Hausdorff dimension of the equilibrium payoffs and relate it to the equilibrium paths and their graph presentation.

Costly Leader Games with a Probabilistically Non-Strategic Leader

2017 ◽  
Vol 19 (02) ◽  
pp. 1750008
Author(s):  
Brishti Guha
Keyword(s):  
Mixed Strategy ◽  
Pure Strategy ◽  
Complete Information ◽  
Information Cost ◽  
Equilibrium Outcome ◽  
Pure Strategy Equilibrium ◽  
Strategy Equilibrium ◽  
Strategic Type ◽  
Simultaneous Move

I consider a two-person costly leader game — in which the follower endogenously chooses whether to buy information about the leader, and a follow-up action — with a twist. With a known probability, the leader is a nonstrategic type. A strategic type leader may choose to masquerade as a nonstrategic type, at a cost. I show that, if the follower’s cost of information is not too large, and the probability of the leader being nonstrategic is neither too large nor too small, this game has no pure strategy equilibrium. Moreover, the equilibrium of the simultaneous-move complete information game is inaccessible as follower information cost converges to zero. There is no equilibrium outcome in which leader advantage is destroyed: however, a mixed strategy equilibrium exists which does preserve leader advantage in the sense that payoffs and strategies converge to those of the sequential-move complete information equilibrium as information cost tends to zero. My results differ from some traditional results in costly leader games, and are due to the interaction of two forces, the “type uncertainty” and the “money down the drain” effects. To my knowledge this is the first paper to integrate behavioral types into costly leader games (other papers considering heterogeneity in type do not consider nonstrategic players).

scholarly journals Tax Competition between Symmetric Countries for Large Asymmetric Investors

2021 ◽  
Author(s):  
Kaushal Kishore
Keyword(s):  
Tax Competition ◽  
Mixed Strategy ◽  
Subgame Perfect Equilibrium ◽  
Complete Characterization ◽  
Tax Revenue ◽  
Perfect Equilibrium ◽  
Initial Stage ◽  
Mobile Capital ◽  
Tax Holiday

Abstract 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

scholarly journals Theory of regional stability as a public good: Examples from Southern Africa

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Fungisai Nota
Keyword(s):  
Public Good ◽  
Subgame Perfect Equilibrium ◽  
Cost Comparison ◽  
Perfect Equilibrium ◽  
Market Failures ◽  
Regional Stability ◽  
Crisis Prevention ◽  
Cost Allocations ◽  
Key Factor ◽  
First Mover

The article examines the interaction of countries in the same region when making efforts to achieve stability. The leader in regional initiatives that foster stability is likely to be the most vulnerable member of the region because in the event of regional instability, the leader member will experience the most detrimental effects. The analysis identifies a key factor - cost comparison - that determines counter-regional instability cost allocations. It is shown that market failures associated with crisis prevention and solving regional instability may be jointly reduced by a vulnerable member. Nevertheless, the subgame perfect equilibrium will still be suboptimal due to leaders who do not internalize the full externalities. Because of the high costs associated with a leader member, she is likely to be the first mover in the game of providing stability, the regional public good, giving its neighbors the opportunity to free-ride.

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