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arxiv: 2409.00832 · v4 · submitted 2024-09-01 · 💰 econ.TH · cs.GT

Satisficing Equilibrium

Bary S.R. Pradelski , Bassel Tarbush This is my paper

Pith reviewed 2026-05-23 20:51 UTC · model grok-4.3

classification 💰 econ.TH cs.GT
keywords satisficing equilibriumbounded rationalitygame theorysolution conceptsNash equilibriumepistemic foundationsdynamic foundationsexistence
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The pith

In satisficing equilibrium each agent plays one of her top k_i actions in response to others' choices.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper defines a new solution concept called satisficing equilibrium. Each player responds to the actions chosen by others by selecting from a personal top set of k_i actions rather than optimizing to a unique best reply. This unifies several existing models of bounded rationality under a single definition. The resulting equilibria produce predictions that differ from those of Nash equilibrium and related concepts. The authors establish existence in most games plus additional economic settings, along with epistemic and dynamic foundations plus empirical testability.

Core claim

In a satisficing equilibrium each agent i plays one of her top k_i actions in response to the actions of the other agents. Our concept unifies models of bounded rationality and yields predictions that differ from canonical solution concepts. We study its theoretical properties and show that it provides sharp predictions, exists in most games as well as in a broad new class of economic environments, admits standard epistemic and dynamic foundations, and is empirically falsifiable.

What carries the argument

The satisficing equilibrium, defined by each agent choosing from her top k_i actions given the profile of others' actions.

If this is right

  • Satisficing equilibria exist in most finite normal-form games.
  • The concept extends to a broad new class of economic environments beyond standard games.
  • Standard epistemic foundations justify the equilibrium as the outcome of common belief in the top-k rule.
  • Dynamic processes such as learning or adjustment lead players to satisficing equilibria.
  • The equilibria produce sharp, testable predictions that differ from Nash equilibrium.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The concept could explain experimental data in which players avoid strict best replies yet still coordinate on limited action sets.
  • It opens the possibility of equilibrium selection based on the size of each player's k_i rather than payoff dominance alone.
  • Empirical work could estimate individual k_i values from choice data under fixed opponent behavior.
  • The framework might apply to mechanism design by relaxing incentive constraints to top-k rather than exact optimality.

Load-bearing premise

Each agent has a well-defined strict ranking over actions that identifies a fixed top-k_i set for any given actions of the others.

What would settle it

An experiment in which observed play lies outside every agent's stated top k_i set for the realized profile of others' actions, even though within-set profiles exist, would falsify the equilibrium concept.

Figures

Figures reproduced from arXiv: 2409.00832 by Bary S.R. Pradelski, Bassel Tarbush.

Figure 1
Figure 1. Figure 1: Latin hypercube ( = = 3). assigned to agent by . We can now use the symbols and their position in the hypercube to assign preferences. For each agent and each action profile a and associated truncated line ¯ a , consider the subset of the line that contains action profiles, a, whose symbols are assigned to agent . Arbitrarily assign preferences such that for these action profiles agent is choosing a th-bes… view at source ↗
read the original abstract

In a satisficing equilibrium each agent $i$ plays one of her top $k_i$ actions in response to the actions of the other agents. Our concept unifies models of bounded rationality and yields predictions that differ from canonical solution concepts. We study its theoretical properties and show that it provides sharp predictions, exists in most games as well as in a broad new class of economic environments, admits standard epistemic and dynamic foundations, and is empirically falsifiable.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper introduces satisficing equilibrium, in which each agent i selects one of her top k_i actions given the actions of the others. It claims the concept unifies models of bounded rationality, yields predictions distinct from canonical solution concepts, exists in most games as well as a broad new class of economic environments, admits standard epistemic and dynamic foundations, and is empirically falsifiable.

Significance. If the central claims hold after clarification of the definition, the work would provide a parameterized yet structured way to capture bounded rationality that unifies disparate models while remaining falsifiable and admitting standard foundations. Existence results in new economic environments would be a notable addition to the literature on solution concepts.

major comments (1)
  1. [Definition (likely §2)] The definition (presumably in §2) requires that, for every action profile of the others, each agent possesses a strict ranking over her actions that identifies a determinate top-k_i set. No structure is given on how k_i is chosen or fixed, nor on resolution of ties or incomplete orders. This renders the equilibrium correspondence potentially empty or set-valued in standard finite games, directly undermining the existence claims in most games and the sharpness of predictions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive report. The single major comment raises an important issue of definitional precision, which we address below with clarifications that strengthen rather than alter the core claims.

read point-by-point responses

  1. Referee: [Definition (likely §2)] The definition (presumably in §2) requires that, for every action profile of the others, each agent possesses a strict ranking over her actions that identifies a determinate top-k_i set. No structure is given on how k_i is chosen or fixed, nor on resolution of ties or incomplete orders. This renders the equilibrium correspondence potentially empty or set-valued in standard finite games, directly undermining the existence claims in most games and the sharpness of predictions.

    Authors: We agree that greater explicitness is warranted. The definition takes as primitives a fixed profile (k_i) for each player together with, for every action profile of the opponents, a strict complete ranking of player i's own actions; the top-k_i set is then the unique k_i highest-ranked actions under that ranking. This is the standard maintained assumption that renders the best-response correspondence single-valued or set-valued in the usual way. The vector k = (k_i) is a model parameter that indexes the degree of satisficing (exactly as the depth parameter indexes k-level reasoning or the quantal-response parameter indexes noise); it is not derived inside the equilibrium concept. Under these maintained assumptions the correspondence that maps opponents' profiles into each player's top-k_i set is non-empty, compact-valued, and upper hemicontinuous on finite action spaces, so Kakutani's theorem directly yields existence of a satisficing equilibrium. The same argument extends to the broader class of environments claimed in the paper. We will add a short paragraph in §2 making these maintained assumptions explicit and noting that extensions to weak orders or endogenous k_i are left for future work; the existence and sharpness results are unaffected. revision: partial

Circularity Check

0 steps flagged

No circularity: satisficing equilibrium introduced by primitive definition; properties derived independently

full rationale

The paper defines satisficing equilibrium directly as each agent playing one of her top k_i actions given others' play. All subsequent claims (unification of bounded-rationality models, existence in most games, epistemic/dynamic foundations, sharp predictions, empirical falsifiability) are presented as consequences of analyzing this definition under standard game-theoretic assumptions. No parameter is fitted to data and then relabeled a prediction, no self-citation chain bears the central load, and no uniqueness theorem or ansatz is smuggled in. The derivation chain is therefore self-contained and does not reduce any result to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The paper adds a new equilibrium definition built on standard game-theoretic structure; k_i functions as a per-player parameter whose value is part of the model specification rather than derived.

free parameters (1)
  • k_i
    The number of top-ranked actions each agent considers; introduced as part of the definition and may be chosen exogenously or fitted per agent or game.
axioms (1)
  • standard math Players have finite action sets and complete, transitive preferences over action profiles that induce a ranking of own actions given others' play.
    Required for the notion of 'top k_i actions' to be well-defined in the normal-form games to which the concept is applied.

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Reference graph

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