Commitment, Learning, and Alliance Performance: A Formal Analysis Using an Agent-Based Network Formation Model

Abstract

Current theoretical arguments highlight a dilemma faced by actors who either adopt a weak or strong commitment strategy for managing their alliances and partnerships. Actors who pursue a weak commitment strategy—that is, immediately abandon current partners when a more profitable alternative is presented—are more likely to identify the most rewarding alliances. On the other hand, actors who enact a strong commitment approach are more likely to take advantage of whatever opportunities can be found in existing partnerships. Using agent-based modeling, we show that actors who adopt a moderate commitment strategy overcome this dilemma and outperform actors who adopt either weak or strong commitment approaches. We also show that avoiding this dilemma rests on experiencing a related tradeoff: moderately-committed actors sacrifice short-term performance for the superior knowledge and information that allows them to eventually do better.

[Supplementary material is available for this article. Go to the publisher's online edition of The Journal of Mathematical Sociology for the following free supplemental resource: Technical Appendix.]

Keywords:

• agent-based modeling
• commitment
• social networks

Acknowledgments

The author order is alphabetical.

We thank Marcel van Assen, Vincent Buskens, Roberto Fernandez, Werner Raub, Ezra Zuckerman, and two anonymous referees, for many useful comments and suggestions.

Notes

¹Here we are not employing the term “mixed strategy” in a game-theoretic sense.

²Our moderate commitment strategy is different than a mixed strategy in the standard game-theoretic sense. In game theory, a mixed strategy (in equilibrium) implies that agents are indifferent between the pure strategies they are mixing over. In our setting, a moderately committed actor is not indifferent between weak or strong commitment, but rather the actor is playing a distinct strategy which is superior in the long run.

³All technical details (including proofs) that are not necessary to understand the main intuitions are contained in the Technical Appendix, available online.

⁴By competence we mean proficiency in some technical field, for example, a profession for individuals or an industry (or geographical market) for firms.

⁵We could let our agents have more than one competence and/or vary in terms of their competence levels. Doing so, however, would complicate our analysis but would not change our substantive conclusions.

⁶We could have specified a more general functional form, but this one is simple, captures the essential features we want to model regarding link formation, and is also concave in each of its arguments. The latter property is convenient once we solve each agent's maximization problem (see footnote 9).

⁷We note that our notion of commitment is unilateral, in the sense defined in Buskens and Royakkers (2002).

⁸This corresponds to “best-response dynamics,” which is one way to converge to a stable Nash equilibrium.

⁹Second-order conditions always obtain, given the concavity implied by Eq. (2).

¹⁰An additional interpretation is that the future is very risky and, thus, agents discount expected values at high rates.

¹¹For an overview of this type of process see Hamilton (2008).

Note. The order of presentation in the table is the same as the order in which parameters and variables apper in the article.

¹²For our two-state Markov chain, the average number of periods until transition is given by 1/(1 − φ), so in our case hidden means are unchanged for an average of 20 periods (we simulate the model for 50,000 periods, which allows for many transitions).

Note. Shows summary statistics for societies composed of three commitment types: weak commitment (WC), moderate commitment (MC), and strong commitment (SC) actors.

Coordination failure stands for the proportion of rounds where no link materialized; average performance per alliance excludes rounds where no link materialized; knowledge/information is measured by how close an actor's beliefs are to true hidden mean payoffs. The network was simulated for 50,000 periods.

¹³In the model, this means a change associated with actor i's competence value, measured by the average , across m(j).

Note. Shows regression coefficients and robust standard errors (in parenthesis). The dependent variables are average overall performance, average performance per alliance, level of coordination failure, and amount of knowledge and information. The independent variables are weak commitment (WC), strong commitment (SC), time since demand change (TIME), and a constant (CONST). The interactions are WC × TIME and SC × TIME.

Average performance per alliance is conditional on at least one link having materialized; coordination failure is the proportion of rounds where an actor did not materialize at least one link; knowledge and information measures how close an actor's beliefs are to true hidden combination payoffs; TIME counts the number of rounds since the last change in hidden combination payoffs. Results obtained by simulating network evolution for 50,000 rounds (same data as in Table 2) and averaging across TIME (note that this is a fully exogenous variable in our model).

¹⁴Also, note that whether an agent revises or not is an exogenous random variable.

Note. Shows average overall performance, coordination failure, and knowledge and information for a mixed society with three commitment levels: weak commitment (WC), moderate commitment (MC), and strong commitment (SC).

Coordination failure stands for the proportion of rounds where no link materialized; knowledge and information is measured by how close an actor's beliefs are to true hidden mean payoffs. The network was simulated for 50,000 periods. All magnitudes besides α are set at the benchmark level.

¹⁵We construct a measure of in-group focus, which for weak commitment actors is the average fraction of time devoted to other weak commitment actors. This measure correlates very negatively with the performance of weak commitment actors (estimate of −0.76).

Note. Shows average overall performance, coordination failure, and knowledge and information in a society composed of weak commitment (WC) actors.

Coordination failure stands for the proportion of rounds where no link materialized; knowledge and information is measured by how close an actor's beliefs are to true hidden mean payoffs. The network was simulated for 50,000 periods. All magnitudes besides α are set at the benchmark level.

¹⁶In many instances, Nash equilibria are not stable; that is, they only correspond to fixed points of the system if the system starts at the equilibrium. This lack of stability is present in our dynamic model, as propositions 2 and 3 illustrate.

¹⁷So, on average, ego would be motivated to keep his current partners.

¹⁸The results from Sections 3.2.2 and 3.2.3 suggest that starting conditions are important. However, we hasten to add that starting conditions matter little in our simulations. Since our societies contain actors who can learn and we provide these actors with the opportunity to do so, starting conditions only matter during the initial rounds of the simulation.