Stable profit sharing in a patent licensing game: general bargaining outcomes

Watanabe, N., & Muto, S. (2008). Stable profit sharing in a patent licensing game: general bargaining outcomes. International journal of game theory, 37(4), 505-523. [working paper 版]

JEL Classification Numbers: C71; D45; D43
Keywords: licensing, coalition structure, bargaining set, core

==noted by yi-nung==

有簡要的 patent licensing problem 的文獻回顧:

Patent licensing problems in oligopolistic markets had been studied only by non-cooperative mechanisms; upfront fee or royalty in Kamien and Tauman (1984, 1986), and auction in Katz and Shapiro (1985, 1986). After these seminal papers, the main concern of researchers was focused on the optimal licensing mechanism that maximizes the licensor’s revenue from a patented technology (See, e.g., Kamien, Oren and Tauman (1992), Muto (1993), Sen (2005) and Sen and Tauman (2007)). On the other hand, licensing agreements are basically contract terms signed by licensors and licensees as negotiation results. This paper hence seeks into the original and practical viewpoint and studies patent licensing as bargaining outcomes.
On this agenda, Tauman and Watanabe (2007, hereafter TW) recently provided the licensor’s payoff in the non-cooperative auction game with an interpretation from a cooperative viewpoint. Their analysis was, however, limited to the asymptotic equivalence. In practice, however, each industry has a finite number of firms operating there. For such a finite industry, Driessen, Muto and Nakayama (1992, hereafter DMN) studied a cooperative game on information trading which is similar to patent licensing。

The Performance of Groups and Individuals in Financial Decision-Making

Christoph Gort and Anke Gerber (2008) “The Performance of Groups and Individuals in Financial Decision-Making." Working Paper No. 460, National Centre of Competence in Research Financial Valuation and Risk Management. [link to PDF];; 提供的 [PDF]

==original Abstract==

On financial markets many investment decisions are taken by groups and not by individuals. The evidence, however, whether groups perform better than individuals, is ambiguous. We analyze the portfolios of groups and individuals in an asset allocation task on an experimental market. We find that groups on average outperform individuals, i.e., achieve higher Sharpe ratios but the difference is not significant. However, there are also large performance discrepancies across groups and the best groups significantly outperform individuals. An important determinant of the success a group in our experiment is the degree of information exchange between group members as a higher level is linked to a significantly better performance.

Stationary Concepts for Experimental 2×2-Games

Selten, Reinhard; Chmura, Thorsten (2008) “Stationary Concepts for Experimental 2×2-Games." American Economic Review, Volume 98, Number 3, June 2008 , pp. 938-966(29). DOI:; 提供的 [PDF];

==notes by yinung==

此文之觀念, 適用於 長期 或 repeated 賽局之均衡解

mixed equilibrium 可視為是動態均衡解 (stationary concept)

Mixed equilibrium has several interpretations. One interpretation is that of a rational recommendation for a one-shot game. Another  interpretation  looks at mixed equilibrium as a result of evolutionary or learning processes in a situation of frequently repeated play with two populations of randomly matched opponents. One may speak of mixed equilibrium as a behavioral stationary concept.

這篇以 2×2 賽局實驗, 比較5種 stationary concept:

Quantal response equilibrium (Richard D. McKelvey and Thomas R. Palfrey 1995)

策略選擇比例是 exponential form

assumes that players give quantal best  responses  to  the behavior of  the others  (see Section  IB).  In  the exponential form of quantal response equilibrium considered here, the probabilities are proportional to an exponential with the expected payoff times a parameter in the exponent.

Action-sampling  equilibrium

從觀察對手的 7 種 (神奇數字) 可能的策略, 來決定自己的最佳策略

…in  a  stationary  situation,  a player takes a sample of seven observations of the strategies played on the other side, and then optimizes against this sample.

Payoff-sampling equilibrium  (Osborne and Rubinstein 1998)


…envisions a  stationary  situation in which a player takes two samples of equal size, one for each of her pure strategies. She then compares the sum of her payoffs in the two samples and plays the strategy with the higher payoff sum…. The best fitting sample size turns out to be six for each of both samples. The name  “payoff-sampling equilibrium" refers to the sampling of own payoffs for each pure strategy.

Impulse balance  equilibrium

和 prospect theory 觀念結合的均衡

proposed  by Selten  is  based  on  learning direction  theory  (Selten  and  Joachim Buchta 1999)…   is  applicable  to the repeated choice of  the same parameter  in  learning situations  in which  the decision maker receives feedback, not only about the payoff for the choice taken, but also for the payoffs connected to alternative actions.
…. The decision maker is assumed to have a tendency to move in the direction of the impulse….

此觀念有別於 reinforcement learning

… that impulse learning is very different from reinforcement learning.

In reinforcement learning, the payoff obtained for a pure strategy played in the preceding period determines the increase of the probability for this strategy. … 完全取決於自己的報酬 (is  entirely based on observed own payoffs)

In  impulse  learning  it  is not  the payoff  in  the preceding period  that  is of crucial importance. It is the difference between what could have been obtained and what has been received, which moves the behavior in the direction of the higher payoff. … 取決於對手的策略和自己的報酬 (requires feedback on the other player’s choice and the knowledge of the player’s own payoff)

均衡成立時, 期望向上和期望向下 impulses 相同, losses 時 impulses 加倍計算
In  the  stationary distribution, expected upward impulses are equal to expected downward impulses. … losses are counted double in the computation of impulses as in prospect theory (Daniel Kahnemann and Amos Tversky 1979).

===五種 equilibrium 之差異===

The five concepts can be thought of as stationary states of dynamic learning models. Learning models differ with respect to their requirements on prior knowledge of the game and on feedback after each period.

reinforcement learning: Nash, quantal response, pay-off sampling equil. 屬之

其它兩種皆需要更多資訊: 自己的報酬 + 對手之選擇

one needs knowledge of one’s own payoff matrix, as well as feedback on the other player’s choice

==original Abstract:==

Five stationary concepts for completely mixed 2×2-games are experimentally compared: Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium (Martin J. Osborne and Ariel Rubinstein 1998), and impulse balance equilibrium. Experiments on 12 games, 6 constant sum games, and 6 nonconstant sum games were run with 12 independent subject groups for each constant sum game and 6 independent subject groups for each nonconstant sum game. Each independent subject group consisted of four players 1 and four players 2, interacting anonymously over 200 periods with random matching. The comparison of the five theories shows that the order of performance from best to worst is as follows: impulse balance equilibrium, payoff-sampling equilibrium, action-sampling equilibrium, quantal response equilibrium, Nash equilibrium.

How Strong Are Weak Patents?*

Farrell, Joseph; Shapiro, Carl (2008) “How Strong Are Weak Patents?" American Economic Review, Volume 98, Number 4, pp. 1347-1369 ( total 23 pages). DOI: [PDF]



We study the welfare economics of probabilistic patents that are licensed without a full determination of validity. We examine the social value of instead determining patent validity before licensing to downstream technology users, in terms of deadweight loss (ex post) and innovation incentives (ex ante). We relate the value of such pre-licensing review to the patent’s strength, i.e., the probability it would hold up in court, and to the per-unit royalty at which it would be licensed. We then apply these results using a game-theoretic model of licensing to downstream oligopolists, in which we show that determining patent validity prior to licensing is socially beneficial.

Do Patent Holdup and Royalty Stacking Lead to Systematically Excessive Royalties?

Einer Elhauge (2008) “Do Patent Holdup and Royalty Stacking Lead to Systematically Excessive Royalties?" Journal of Competition Law & Economics, 4 (3): 535-570. doi: 10.1093/joclec/nhn027; link to CLER. download PDF.

==notes by yinung==

see also Shapiro (2010).

這篇亦有提到 patent 類似分餅 ultimatum game 遊戲

==original Abstract==

Some recent literature has concluded that patent remedies result in systematically excessive royalties because of holdup and stacking problems. This article shows that this literature is mistaken. The royalty rates predicted by the holdup models are often (plausibly most of the time) below the true optimal rate. Further, those predicted royalty rates are overstated because of incorrect assumptions about constant demand, one-shot bargaining, and informational symmetry. Although this literature concludes that overcompensation problems are exacerbated by doctrines measuring damages using past negotiated royalties, in fact such doctrines exacerbate undercompensation problems. Undercompensation problems are further increased to the extent that juries cannot measure damages with perfect accuracy, a problem that persists even if damages are just as likely to be overestimated as underestimated. Nor do the royalty rates predicted by the holdup model apply if there is competition in the downstream product market or upstream market for inventions. Royalty stacking does not lead to royalties that exceed the optimal rate, contrary to this literature, but in fact tends to produce royalties that are at or below the optimal rate.

Does commitment or feedback influence myopic loss aversion? An experimental analysis

Thomas Langer, Martin Weber, (2008),Does commitment or feedback influence myopic loss aversion? An experimental analysis, Journal of Economic Behavior & Organization, 67, 810–819. LINK TO JEBO

Notes by yinung

這篇將投資期間長/短 , 和資訊迴饋頻率 (frequent/infrequent) 兩種因素進行交叉實驗, 實驗結果和 Bellemare et al. (2005) 的並不十分一致; Bellemare et al. (2005) 主要實驗設計在於資訊迴饋頻率 frequent/infrequent, 其 treatment 有三種:

H: 投資期間1期, 資訊迴饋頻率每1期
M: 投資期間3期, 資訊迴饋頻率每1期
L: 投資期間3期, 資訊迴饋頻率每3期

Bellemare et al. (2005) 實驗結果是: 投資額度 L~M>H

本文有 3 個主要結論:

  • 定期定額 (binding decisions, 連續3期) 可降低短視現象 (myopic, 對風險資產投資比例較高), 且這個現象不會隨著時間增長而改變
First, binding decisions cause people to be less myopic, perhaps because they must think through the implications of a longer time horizon.
  • 提供較低頻率報酬結果迴饋資訊, 有助於降低短視現象, 即隨著時間增長, 可使持有/投資風險資產比例升高
Second, providing less frequent feedback seems to help people learn over time that it is better to go with the risky prospect (i.e. to be less myopic).
  • 定期定額和資訊迴饋頻率之間似乎有複雜的混合效果 (mixed treatment effects):
    • 最強效果 (應該指的是投資風險資產比例最高) 出現在 “定期定額和高資訊迴饋頻率"
    • 「定期定額和資訊迴饋頻率」 下之投資風險資產比例 > 「定期定額和資訊迴饋頻率」 下之投資風險資產比例
Third, there is no simple main effect from combining commitment and feedback, but an interaction between these two variables.

It seems that if people are committed to their decisions, more frequent feedback is helpful because over time it becomes more salient that occasional losses are outweighed by ultimate gains.


只要資訊頻率降低, 即可讓投資風險資產意願提高…
Our findings show that varying the information condition alone suffices to induce behavior that is in line with the hypothesis of Myopic Loss Aversion.
In this paper, we argue that the relation between myopia and the attractiveness of a lottery sequence is less general than previously suggested in the literature.
主要 hypotheses


Hypothesis 3

. For all treatments, the proportion of wealth α(t) invested in the risky asset increases over time.


實驗結果 (圖、表)

image image image image image image


Empirical research has demonstrated that a lower feedback frequency combined with a longer period of commitment decreases myopia and thereby increases the willingness to invest in a risky asset. In an experimental study, we disentangle the intertwined manipulation of feedback frequency and commitment to analyze how each individual variable contributes to the change in myopia and how they interact. We find that the period of commitment exerts a substantial impact and the feedback frequency a far less pronounced impact. There is a strong interaction between both variables. The results have significant implications for real world intertemporal decision making.


Financial markets in the laboratory: an experimental analysis of some stylized facts

Andrea Morone(2008) “Financial markets in the laboratory: an experimental analysis of some stylized facts," Quantitative Finance, Volume 8, Issue 5, pages 513-532. [working paper PDF]; Source: DOI

實驗說明: An example of the Power Point presentation can be found at

Summary by Yinung

此篇是以實驗建構 single-unit double-auction 財務市場,進行交易,再檢驗成交價的 times-series 性質, 包含:

1. Normality (JB-test)
2. Kurtosis
3. ADF tests
4. Hill estimator (for testing tail distribution)
5. Volatility clustering
6. autocorrelation (returns, squared returns, absolute returns, Box-Ljung)


1. 只用一般的 double-auction 交易市場之設定 + 資訊品質 (猜中機率) 高/低 + 獲得資訊成本高/低,似乎沒有明確找到財務交易 return 的 AR丶GARCH 等常見之資料型態 (stylized facts),也沒有分析為何導致此現象之分析說明

2. 因為在 10 periods 中, 每一個 period 都是獨立, 不解如何能以 time-series 的方式來進行相關檢定?






image image
image image



Pagan (1996) provided an authoritative survey of these stylized facts and of the econometric techniques how to
treat them.

Various experimental studies attempted to analyse the role of information within financial markets….  can categorize these studies into three groups:

  • Studies addressing the issue of dissemination of information from a group of identical informed agents (insiders) to a group of identical un-informed agents.
  • Studies addressing the issue of aggregation of different pieces of information owned by different traders and its dissemination.
  • Studies addressing the issue of information’s production.

Plott and Sunder (1982) studied the dissemination of information by running an experiment

Plott and Sunder (1988) designed an experiment on information aggregation

Cobweb model

The extremely important aspect of expectation formation and learning in dynamic experimental markets with expectations feedback was partially addressed by Smith, Suchanek and Williams (1988). Recently, Hommes et al (1999, 2000) and Sonnemans et al (1999) tested for expectation formation in a cobweb model (for a survey see also Hommes, 2001).

herd behaviour

The experiment is based on at least two important strands of literature.

  • The first of these strands is that of herd behaviour in a non-market context. The key references are Banerjee (1992) and Bikhchandani, Hirshleifer and Welch (1992), both of which showed that herd behaviour may result from private information not publicly shared.
  • The second strand of literature motivating this paper is that of information aggregation in market contexts. A very early reference is the classic paper by Grossman and Stiglitz (1966) which showed that uninformed traders in a market context can become informed through the price in such a way that private information is aggregated correctly and efficiently.

A summary of the progress of this strand of literature can be found in the paper by Plott (2000).

Original abstract

This paper provides experimental evidence explaining a number of stylized facts associated with the behaviour of financial returns, in particular the fat tailed nature of their distribution and the persistence in their volatility. By means of a laboratory experiment, we investigate the effect of the quantity and quality of information present in a financial market upon its stylized facts, showing how both the quality and quantity of information might have an impact on volatility clustering and the emergence of fat tail returns.

Policies Designed for Self-Interested Citizens May Undermine “The Moral Sentiments”: Evidence from Economic Experiments

Samuel Bowles (2008) Policies Designed for Self-Interested Citizens May Undermine “The Moral Sentiments”: Evidence from Economic Experiments, Science 20 June 2008: Vol. 320 no. 5883 pp. 1605-1609. DOI: 10.1126/science.1152110.

Notes by Yi-Nung

這是一篇很典型的「文獻回顧型」的 paper (發表在很棒的 Science 期刊)…


外顯動機 (explicit incentives) 和道德動機 (ethical motives) 是且互補性 (complements);亦即,不能只依賴「外顯動機」當做趨使人們做出正確 (係指 social optimal) 決策之方法; … 本文提及的實驗證明,外顯動機機制會降低道德感 (… Incentives undermine ethical motives…)



Original Abstract

High-performance organizations and economies work on the basis not only of material interests but also of Adam Smith’s “moral sentiments.” Well-designed laws and public policies can harness self-interest for the common good. However, incentives that appeal to self-interest may fail when they undermine the moral values that lead people to act altruistically or in other public-spirited ways. Behavioral experiments reviewed here suggest that economic incentives may be counterproductive when they signal that selfishness is an appropriate response; constitute a learning environment through which over time people come to adopt more self-interested motivations; compromise the individual’s sense of self-determination and thereby degrade intrinsic motivations; or convey a message of distrust, disrespect, and unfair intent. Many of these unintended effects of incentives occur because people act not only to acquire economic goods and services but also to constitute themselves as dignified, autonomous, and moral individuals. Good organizational and institutional design can channel the material interests for the achievement of social goals while also enhancing the contribution of the moral sentiments to the same ends.