James D. Laing

Prediction logic: A method for empirical evaluation of formal theory†

This paper proposes an approach to data analysis that assists the investigator in discriminating among specific relations corresponding to alternative scientific predictions about qualitative variates.

On automated discovery of models using genetic programming: bargaining in a three-agent coalitions game

The creation of mathematical, as well as qualitative (or rule-based), models is difficult, time-consuming, and expensive. Recent developments in evolutionary computation hold out the prospect that, for many problems of practical import, machine learning techniques can be used to discover useful models automatically. The prospects are particularly bright, we believe, for such automated discoveries in the context of game theory. This paper reports on a series of successful experiments in which we used a genetic programming regime to discover high-quality negotiation policies. The game-theoretic context in which we conducted these experiments-- a three-player coalitions game with sidepayments--is considerably more complex and subtle than any reported in the previous literature on machine learning applied to game theory.

Coalitions and payoffs in three‐person sequential games: Initial tests of two formal models

In this paper we develop two formal models predicting coalitions and payoffs among rank striving players in a sequential three‐person game. We test the models’ predictions with data from a laboratory study of eleven male triads. Each triad plays a sequence of games; in each game a two‐person coalition forms and divides the coalitions point value between the two coalition partners. Participants know that the sequence of games will end without warning at a randomly chosen time; at the sequences end each players monetary payoff is a linear function of the rank of his accumulated point score, relative to those of the other members of his triad. The complexity of this situation prevents players and analysts from representing it as a single game; thus they are unable to use n‐person game theory to identify optimal strategies. Consequently, we assume that players, unable to develop strategies that are demonstrably optimal in the long run, adopt certain bargaining heuristics and surrogate short run objectives....

On automated discovery of models using genetic programming in game-theoretic contexts

The creation of mathematical, as well as qualitative (or rule-based), models is difficult, time-consuming, and expensive. Recent developments in evolutionary computation hold out the prospect that, for many problems of practical import, machine learning techniques can be used to discover useful models automatically. These prospects are particularly bright, we believe, for such automated discoveries in the context of game theory. This paper reports on a series of successful experiments in which we used a genetic programming regime to discover high-quality negotiation policies. The game-theoretic context in which we conducted these experiments-a three-player coalitions game with sidepayments-is considerably more complex and subtle than any reported in the literature on machine learning applied to game theory.<<ETX>>

Winners, blockers, and the status quo: Simple collective decision games and the core

3. SummaryThis essay considers a general class of collective decision problems that may be represented as simple collective decision games. This analysis departs from the emphasis of the earlier literature on simple cooperative games by giving special attention to situations in which blocking coalitions are possible. We define a procedure for constructing the core of such games. We establish results demonstrating that, in simple games in which blocking coalitions are possible, the relative attractiveness of the no-decision or status quo outcome delimits the core. We prove theorems specifying necessary and sufficient conditions for any simple collective decision game to possess a nonempty core and for the status quo to belong to the core. The last theorem in this essay has special significance for solution theory about simple collective decision games. Any point in the core has a claim for stability if that point somehow becomes the tentative outcome of negotiations. But, mathematically, the core is a static equilibrium concept that, as such, does not specify a process leading to any feasible alternative as the tentative outcome. However, the status quo is the natural starting point of negotiations in collective decision making. Therefore, one can make a special claim for the stability of the status quo if it belongs to the core.

Viable Alternatives to the Status Quo

Collective decision making occurs within constraints associated with the option to maintain the status quo. If this default option is sufficiently attractive to participants and the rules imply that blocking coalitions can form, then these constraints delimit the decision problems core solution—the most important solution concept in the theory of cooperative games. The results presented in this article demonstrate that these constraints have important effects on the outcomes of collective decisions, regardless of whether or not the problem has a core solution. In the laboratory situation, a five-person committee makes a separate decision under four-fifths majority rule about each in a series of six distinct choice problems. This design enables us to analyze the independent effects of variations in the status quo on the outcomes of collective-decision problems in which blocking coalitions are possible, controlling for whether or not the game has a core solution.

Metastability and solid solutions of collective decisions

Abstract A fundamental maxim for any theory of social behavior is that knowledge of the theory should not cause behavior that contradicts the theorys assertions. Although this maxim consistently has been heeded in the theory of noncooperative games, it largely has been ignored in solution theory for cooperative games. Solution theory, the central concern of this paper, seeks to identify a subset of the feasible outcomes of a cooperative game that are ‘stable’ results of competition among participants, each of whom attempts to bring about an outcome he favors, rather than to prescribe ‘fair’ outcomes that accord with a standard of equity. We show that learning by participants about the solution theory can cause the outcomes identified as stable by certain solution concepts to become unstable, and discover that an important distinction in this regard is whether the solution concept requires each element of the solution set to defend itself against alternatives rather than relying on other elements for its defense. Finally, we develop a concept of ‘solid’ solutions which have a special claim for stability. The unifying theme of this paper concerns the sense in which certain outcomes of a cooperative game may be regarded as stable, and the extent to which this stability requires that the players are ignorant of the theory. Although the issues raised here have implications for the theory of cooperative games in general, Section 1 establishes the focus of the analysis on collective decision games. Section 2 develops some general perspectives on solution theory which are used in Sections 3 and 4 to evaluate the Condorcet solution, the core, the robust proposals set, von Neumann- Morgenstern solutions and competitive solutions. Section 5 presents the concept of a solid solution and relates this idea to the solution concepts reviewed earlier. We demonstrate that in general a solution concept has a strong claim to stability only if it is solid. Finally, Section 6 concludes by indicating that the basic argument also can be applied to Aumann and Maschlers bargaining sets and, more generally, to solution theory for any cooperative game.

Coalitions and Payoffs in Three-Person Supergames under Multiple-Trial Agreements

We outline here two formal models that predict coalitions and payoffs in sequential three-person games. The theories share the same structure, differing only in the planning horizon that we assume players use in calculating their strategies. Proceeding from a priori assumptions concerning the players’ preference orderings over the various possible coalition outcomes and heuristic rules-of-thumb the players use in calculating their strategies, and assumptions about the nature of the bargaining process among the three players, the models predict both the probability that each coalition forms and the division of payoffs between coalition partners.

Contending “signals” in coalition choice 1

During negotiations for coalitions, each actor presumably searches his decision environment for organizing principles—signals—which, if present, would turn the negotiations in his favor. With only one prominent signal, we expect it to determine the nature of agreements, but things may be different with multiple signals. Data from four studies of a weighted‐majority game, two using only relative status of winnings in the game as the incentive (i.e., rank position of points accumulated) and two also using monetary reward as an incentive, are analyzed. Both relative status and resources (weights) were apparent to subjects in the studies. Results for coalitions and for payoffs show that a theory based on resources as the signal and one based on status as the signal both separately achieve success in the same bodies of data. As expected, the status‐signal theory better predicted coalitions in the two status‐reward studies, and the resource‐signal theory better predicted in the monetary‐reward studies. However,...

Bargaining Processes and Coalition Out comes

Specification of the three-person coalition bargaining process model (Friend, 1973) occurs in four steps: presentation of (a) the communication typology, (b) the communication inference rules, (c) the decision-making functions, and (d) the main processing rules. The semantics of bargaining are represented by three content categories: OFFER, ACCEPT, and REJECT. Each communication has an associated sender (I) and intended receiver (J) and, in the case of offers, the magnitude of the prize being offered to J (SPLIT). At any point in time, offers are declared to be active (no response as yet), accepted, refected or withdrawn. Aside from a bookkeeping rule to track the direct consequences of communications, two inference rules are postulated which take into account the existing state of affairs due to past communications: (II) If there is an offer from I to J which is active or accepted and if J makes an offer to I or to K or if J accepts an offer from K, then the offer from I to J is rejected. (12) If an offer from I to J is active or accepted and if I makes another offer to J or to K, then the offer from I to J is withdrawn. The process theory asserts that a player must be able to perform three kinds of decisions : He must be able to (a) generate offers, (b) evaluate single offers, and (c) perform a relative evaluation of two offers. The names given to the subprocesses which produce these decisions are GENOFF, EVAL and REVAL, respectively. More is said about these processes later. The framework of the processing model is completed by the specification of nine processing rules which call forth GENOFF, EVAL and REVAL in appropriate contexts (ME is the variable representing a player’s identity): (Rl) If there are no active or accepted offers, then GENOFF. (R2) If there is an active offer not including ME, then GENOFF. (R3) If an accepted offer does not include ME, then GENOFF. (R4) If a single active offer is directed to ME, then EVAL. (R5) If two active offers include ME, then REVAL. (R6) If an active and accepted offer include ME, then REVAL. (R7) If there is