|
on Game Theory |
| By: | Giulio Salizzoni; Domenico Mergoni Cecchelli; Edward Plumb; Maryam Kamgarpour; Galit Ashkenazi-Golan |
| Abstract: | While infinitely repeated games admit a rich set of Nash equilibria, finitely repeated games typically have a much smaller and often inefficient one. We show how to enlarge this set using deposits: in each period a player may place a refundable sum with a neutral intermediary, returned when the game ends and forfeited following a deviation. Paying these deposits is voluntary and incentive compatible at every stage, so no commitment by the players is assumed, the only commitment required being that of the intermediary to a refund rule fixed before play begins. The mechanism sustains payoff profiles more efficient than those of the standard equilibria, without altering the underlying game and without transfers between players. We demonstrate it on the prisoner's dilemma, a congestion game, and a public goods game, all settings where cooperation cannot emerge in the standard finitely repeated version. We also apply it to a dynamic common-pool resource, suggesting that the construction extends beyond repeated stage-games. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.27536 |
| By: | Cont, Rama (Mathematical Institute, University of Oxford); Hu, Anran (IEOR Department, Columbia University, New York) |
| Abstract: | We investigate how the framework of mean-field games may be used to study strategic interactions in large heterogeneous populations. Starting from a partition of the player population into groups, we introduce an intermediate finite-player game of mean-field type and derive explicit non asymptotic bounds for the average exploitability of strategy profiles obtained by lifting strategies from the associated multi-population mean-field game. The approximation error decomposes into two components: a finite population mean-field error, controlled by empirical-measure approximation within each group, and a heterogeneity error measuring deviations of the original players' rewards and transition dynamics from their group-level approximations. Our results apply to compact state and action spaces and allow heterogeneous deterministic initial states within each population. We further study the resulting tradeoff between group size and intra-group heterogeneity. In a parametrized heterogeneous setting, the choice of partition minimizing the resulting certified upper bound can be formulated as a mixed-integer second-order cone program. In the large-population regime, this problem is shown to be related to K-means clustering. |
| Keywords: | stochastic games, mean-field games, mean-field approximation, multi-player dynamic games, Nash equilibrium, homogenization |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:amz:wpaper:2026-22 |
| By: | Daniel Eckert (University of Graz, Austria) |
| Abstract: | In this note we make the claim that Karl Menger's "Logic of Ethics" in his 1934 monograph "Moral, Wille und Weltgestaltung" was not only a souce of methodological inspiration for Oskar Morgenstern's contribution to the development of game theory, but can actually be considered an anticipation of a game theoretic approach to coalition formation known today as hedonic games. |
| Keywords: | ethics, coalition formation, game theory, partitions, cooperative game theory, hedonic games |
| JEL: | B23 C71 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2026-15 |
| By: | Zitian Wang; Istiak Ahmed; Patarasate Unjitwattana; Emily Yunxi Xie; Meng-Jhang Fong; Po-Hsuan Lin |
| Abstract: | How level-0 players behave and how they are perceived by higher-level players are central questions in the literature on level-k models of boundedly rational strategic reasoning. To study these twin questions, we apply the intra-team communication method developed by Burchardi and Penczynski (2014) to identify level-0 actions and beliefs in the canonical beauty contest game and in a variant of the 11-20 game of Goeree et al. (2018), in which behavior appears inconsistent with the standard level-k model. In the beauty contest game, we replicate Burchardi and Penczynski (2014)'s finding that elicited level-0 beliefs align with observed level-0 actions. In the variant of the 11-20 game, however, elicited level-0 beliefs and observed level-0 actions diverge, and both depart from the standard level-0 assumption, suggesting a complementary explanation for the behavioral pattern documented by Goeree et al. (2018). |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.18069 |
| By: | Michael Ostrovsky; Andrzej Skrzypacz |
| Abstract: | We revisit the classic result on the (non-)existence of pure-strategy Nash equilibria in the Generalized First-Price Auction for sponsored search advertising and show that the conclusion may be reversed when ads are ranked based on the product of stochastic quality scores and bid amounts, rather than solely on the bids or on the product of bids and deterministic quality scores. Moreover, the expected revenue in the pure strategy equilibrium of the Generalized First-Price Auction may substantially exceed that of the Generalized Second-Price Auction, although under some conditions the relation may also be reversed. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.00334 |
| By: | Sumana Kundu (Indira Gandhi Institute of Development Research) |
| Abstract: | We study firms' strategic choice between transparent and opaque personalized pricing in a duopoly with differentiated network goods with both within-firm and between-firm network effects. Under transparent pricing, consumers observe prices offered to others and internalize the resulting network benefits. In contrast, under opaque pricing, such information remains private, limiting consumers' ability to coordinate their purchasing decisions. Consumers are heterogeneous in baseline valuations and firm-specific preferences. We show that, unlike in monopoly settings, opaque pricing is more profitable than transparent pricing in competitive markets whenever firms' networks are not perfectly compatible. This is because transparency intensifies competition by allowing consumers to respond strategically to expected network participation, whereas opacity doesn't allow the same, enabling firms to sustain higher prices. Endogenizing firms' choice of pricing schemes, we show that when firms' network compatibility is relatively high, or consumers are sufficiently heterogeneous, or firms' marginal cost differences are high, (Opaque, Opaque) is the unique Nash equilibrium. In other cases, firms' pricing schemes become strategic complements, giving rise to both (Transparent, Transparent) and (Opaque, Opaque) as Nash equilibria; however, the latter is Pareto-dominant. We further show that transparent pricing can induce strategic subsidization, whereby a high-cost firm prices below cost for low-valuation consumers to signal stronger network benefits. In a sequential purchasing environment, we show that firms earn higher profits than under transparent pricing, but lower profits than under opaque pricing. Finally, we show that prohibiting personalized pricing always lowers firms' profits in a duopoly. |
| Keywords: | Personalized pricing, Transparent pricing, Opaque pricing, Network effects, Consumer heterogeneity, Nash equilibria |
| JEL: | D43 D82 L10 L13 L21 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:ind:igiwpp:2026-013 |
| By: | Mustapha Nyenye Issah; Paramahansa Pramanik |
| Abstract: | We develop a continuous-time entry-deterrence game in which market demand evolves according to the Chan-Karolyi-Longstaff-Sanders (CKLS) stochastic differential equation, allowing mean reversion and state-dependent volatility. An incumbent with privately known strength strategically chooses advertising and promotional expenditures to influence a potential entrant's beliefs, while the entrant faces a costly, irreversible entry decision and optimally waits until market conditions justify participation. Within a dynamic Stackelberg setting, Bayesian learning, asymmetric information, stochastic demand, and strategic controls jointly determine entry and signaling behavior. Using a Feynman-type path-integral control formulation, we characterize a Markovian Nash feedback equilibrium for the firms' expenditure strategies. Our contribution is to integrate CKLS demand uncertainty, private information, irreversible entry, Bayesian belief updating, and path-integral feedback control within a unified continuous-time entry-deterrence framework, while providing a computational alternative to direct Hamilton-Jacobi-Bellman (HJB) approach. We illustrate the framework empirically using 2010-2024 revenue data for Enterprise Products Partners and Targa Resources. The resulting trajectories are qualitatively consistent with the model's predictions, exhibiting persistence, recovery after adverse shocks, and distinct responses associated with different competitive positions, while supporting the model's strategic mechanisms under uncertainty. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.17273 |
| By: | Karle, Heiko; Schumacher, Heiner; Volund, Rune |
| Abstract: | We study a simple bargaining model in which the sender can make an early offer to the receiver. Initially, the sender has private information about the value of the receiver's outside option. The receiver learns this value before she chooses between the sender's early offer and her outside option. Nevertheless, if the receiver is expectation-based loss averse, the sender can persuade her to accept an offer that is inferior to her outside option. This result is due to the interaction of two effects: the attachment effect that makes it costly for the receiver to reject an offer that she planned to accept, and the uncertainty effect which renders the acceptance of the sender's offer as the preferred plan since it creates peace of mind at an early stage. If the receiver faces uncertainty in multiple dimensions, the main result holds for all degrees of loss aversion. Thus, expectation-based loss-averse preferences imply that there is scope for persuasion through signaling even if the receiver has all payoff-relevant information at the decision stage. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19247 |
| By: | Federico INNOCENTI; Nicola DONI; Domenico MENICUCCI |
| Abstract: | This paper is about a two-bidder auction setting with endogenous and costly entry in which, before the bidders' entry decisions, the seller may release information about the object on sale. This information affects each bidder's belief about the own distribution of value for the object on sale, hence it affects the bidder's incentive to enter. The seller uses a second price auction and we consider the class of unrestricted information structures using the techniques of information design in which the seller sends private messages to the bidders. We characterize the optimal information structure, which optimally trades off providing rents to the bidders in favorable (to the bidders) states of the world against inducing entry of all bidders in other states of the world (in order to generate a positive auction revenue). We compare the optimal information structure with some specific information structures examined in the literature and then show that a restriction to public messages hurts the seller significantly. We also show that using a first price auction allows the seller to earn the same revenue as when a second price auction is used. We then allow the seller to use an entry fee and jointly optimize, under some restrictions, with respect to the entry fee and the information structure. In this case the seller does not need to induce entry of all bidders to earn a positive revenue, and indeed induces entry of a single bidder, who is required to pay a high entry fee, if the entry cost is not small. But if the seller can also use a reserve price, then it is optimal to (almost) fully subsidize the entry cost and use the reserve price to extract all the bidders' rents while inducing the socially optimal entry. |
| Keywords: | Procurement Auctions, First-Price Auction, Second-Price Auction, Pre-Auction Investment, Strategic Effect, Auction Ranking. |
| JEL: | D44 D82 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:frz:wpaper:wp2026_09.rdf |
| By: | Foivos Savva; Michele Lombardi; Ritesh Jain |
| Abstract: | Can altruism serve as the behavioral foundation for efficient institutional design? We study full implementation in Berge equilibrium, the solution concept that formalizes strategic altruism: each agent's opponents collectively maximize her payoff. While Berge equilibrium resolves the Prisoner's Dilemma and can eliminate cooperation failures in social dilemmas, we show that this optimism does not survive the move from individual behavior to institutional design. First, we show that the weak Pareto optimal rule is not implementable in Berge equilibrium. Second, on the unrestricted domain of strict preferences, any social choice rule that is both weakly Pareto efficient and implementable in Berge equilibrium must be dictatorial. Finally, we show that Berge implementability is strictly more demanding than Nash implementability: every social goal achievable under strategic altruism is also achievable under self-interest, but not vice versa. The very feature that makes Berge equilibrium appealing at the behavioral level, that is, opponents protecting each agent's payoff, is precisely what forecloses efficient, non-dictatorial institutions at the design level. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.24774 |
| By: | Olga Rospuskova; Omer Tamuz; Jake Zhang |
| Abstract: | We study global games in which agents coordinate locally, with their social network neighbors, contingent on a favorable state. Before acting, agents learn the private signals of all agents within network distance $r$. As $r$ grows, every agent learns the state, but efficient coordination depends on higher-order beliefs, which are shaped by the geometry of the network. We introduce network common learning, a network analogue of common learning, and show that it is attained when neighboring agents' observations differ by many signals, as on the two-dimensional grid, but fails on networks with informational bottlenecks, such as the line, where only the safe action survives in equilibrium. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.28821 |
| By: | Nandish Patel (Indira Gandhi Institute of Development Research) |
| Abstract: | We study entry in a differentiated-product Bertrand industry in which firms are privately informed about their marginal costs. We show that policies that facilitate entry, such as per-unit subsidies to entrants increase expected output and total welfare. Under Bayes-Bertrand competition, firms condition their pricing decisions on the expected costs of their rivals rather than on realized costs. In this environment, facilitating entry for relatively inefficient types raises the expected output of inframarginal firms and incumbents, owing to the strategic complementarity of prices. When all firms simultaneously decide whether to enter, it is optimal to allow all potential entrants to participate. |
| Keywords: | Bayes-Bertrand oligopoly, Differentiated products, Market entry, Welfare maximization |
| JEL: | D43 D82 L13 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:ind:igiwpp:2026-011 |
| By: | Vravosinos, Orestis; Vives, Xavier |
| Abstract: | The lattice-theoretic approach has had a significant impact in all fields of economics, being progressively incorporated into the standard toolbox. This paper presents a selective survey with an emphasis on basic tools, some important results, and applications in industrial organization, dynamic games, games of incomplete information, and mechanism design. Frontier theoretical research employing lattice-theoretic methods continues to be developed in areas such as mean-field games and information design. |
| JEL: | C62 C72 D01 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19214 |
| By: | Andreas L\"offler; Stefan Steins |
| Abstract: | Rising interest rates can expose life insurers to surrender risk by reducing the market value of their assets and raising policyholders' outside returns. This paper develops a minimal model of an insurance-specific run mechanism in which strategic interaction arises because early surrenders can deplete the asset pool backing continuation values. We analyze a strategic surrender game in which a run is an equilibrium outcome determined jointly by asset values, contractual surrender claims, and payoff-dependent continuation benefits. The model yields closed-form interest-rate thresholds for fundamentals-driven and self-fulfilling runs. Thinner capitalization weakly lowers the joint-surrender cutoff. Continuation benefits raise surrender thresholds but can also create strategic complementarity. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.20982 |
| By: | Yuta Kido; Yohsuke Ohtsubo |
| Abstract: | Reputation and institutional certification are the two main trust mechanisms under information asymmetry, yet their interaction remains poorly understood. We analyze nearly one million fixed-price eBay listings of Pokemon cards, where sellers choose among three signals: third-party grading (institutional certification), self-grading (a self-claimed condition description), or no signal. We show that self-grading and third-party grading dominate distinct regions of the reputation-value space, with the self-grading region widening as reputation rises. Reputation also amplifies the price premium of self-grading but not that of third-party grading. We develop a signaling game in which a false self-claim carries an ex-post cost proportional to reputation, whereas certification carries an ex-ante cost independent of reputation. These costs split the reputation-value space into equilibrium regimes that explain both patterns. The two mechanisms are therefore substitutes within a transaction yet complements across the market, replacing the reputation-versus-institution dichotomy with a regime structure set by reputation and value. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.17312 |
| By: | Constantine Sorokin; Alexander Nesterov; Alexei Savvateev |
| Abstract: | In organized crime, membership moves fastest, deterrence capacity moves more slowly, and division norms move slowest. We model this as a three-stage game: division norms fix how every possible coalition divides its proceeds; the authority then attaches deterrence capacity to named members, before knowing which coalition will form; membership adjusts last, around whoever remains undeterred. Under population-monotone division, the minimum deterrence budget is the cost of a shortest dismantling path, removing one member at a time. When the Shapley value is population monotone, it uniquely maximizes this budget by making every path equally costly. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.13327 |
| By: | Edgar J. Sánchez-Carrera; Elvio Accinelli; Humberto Muñiz |
| Abstract: | Tourism is often promoted as a route to local development, yet many destinations combine persistent visitor flows with poverty, informality, insecurity, and weak local spillovers. This paper develops a coordination model to explain that paradox. Governments choose between public investment and extraction, residents between formal and informal participation, and tourists between local engagement and enclave consumption. Tourism-led growth emerges only when these choices are mutually reinforcing. Otherwise, individually rational responses can stabilize a low-development regime in which institutions remain weak, residents stay informal, and visitor spending bypasses local supply chains. The static game admits both a low-development equilibrium and a high-development equilibrium. Embedding the model in replicator dynamics shows how thresholds, initial conditions, and coordinated reforms shape transitions between traps and more inclusive regimes. The paper contributes a mechanism-based framework for understanding why tourism can be economically central and yet fail to generate broad-based local development. |
| Keywords: | Tourism-led growth; poverty traps; coordination failure; informality; enclave tourism; evolutionary game theory. |
| JEL: | C72 C73 O17 O43 R11 Z32 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:frz:wpaper:wp2026_19.rdf |
| By: | Jobst Heitzig |
| Abstract: | We study a dynamic coalition-formation process in the tradition of Konishi and Ray (2003): players repeatedly form and dissolve binding agreements, evaluate states by discounted long-term expected payoffs, and hold self-confirming beliefs about the process. States and payoff sharing follow Heitzig and Kornek (2018): a state is a hierarchy of nested agreements; agreements are formed by merging existing top-level coalitions, and are terminated together with all agreements containing them; and the members of a new agreement share the surplus it generates, measured against the state without that agreement. All payoff assumptions are structural. We prove that every grand state ever reached is absorbing, and that every absorbing state is grand, for every discount factor. A grand state is actually reached, almost surely, in three cases: small discount factors; three players; and, for any number of players and all discount factors, whenever every player prefers every grand state to every non-grand state in static payoffs, as when distributional stakes are smaller than each player's share of the efficiency gain. Otherwise the process can fail only by cycling for ever among non-grand states. We give exact necessary conditions on such a cycle, and show that for a fixed candidate cycle they reduce to a finite system of linear inequalities in the static payoffs, so the question is decidable. Solving it yields a counterexample: with four players and discount factor one half, under either termination rule, there is an equilibrium that cycles for ever, so the grand coalition need not form. The example survives a far-sighted variant of the sharing rule under which merging raises every player's discounted long-term payoff, not only the static one; there the merge is blocked purely by a better move available to a subgroup. Whether arrival can fail as the discount factor tends to one remains open. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.17766 |
| By: | Bo Chen; Rui Gao; Jingfeng Lu; Zhewei Wang |
| Abstract: | A team-contest designer values output rather than expenditure; nonlinear conversion makes the distinction consequential. We study two non-pecuniary instruments in majority-rule contests decided by pairwise all-pay battles with private abilities: disclosing resolved outcomes and splitting the battle schedule into finer blocks. Neither changes a battle's average pivotality; each only redistributes it across histories. Under nested information structures, this redistribution makes equilibrium ability-scaled expenditure weakly more dispersed player by player without changing its mean; expected aggregate expenditure is invariant across all designs considered. The resulting convex-order comparison ranks expected total output: convex output costs favor no disclosure and coarser temporal structures, concave costs favor full disclosure and finer ones, and linear costs make both comparisons neutral. The rankings hold for finite-support and smooth continuous-type ability distributions. The mechanism extends to degree-zero component contest technologies with a unique equilibrium outcome distribution. No and full disclosure bound every admissible public garbling. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.22694 |
| By: | Qian Cao; Yifei Sun |
| Abstract: | Opposing advocates may be unable to fabricate evidence but can choose which true observations to present. We study how a court, editor, or platform should divide potential exposure between an advocate who prefers a higher decision and one who prefers a lower decision. Each advocate controls a separate evidence pool, exposure is committed before the state and evidence are known, and a selection-naive receiver averages displayed observations. Under baseline linear preferences and common knowledge of the realized pools, all Nash equilibria in every finite pool induce the same action and common disclosure bar: the upward advocate reveals observations above it and the downward advocate those below it. Attention therefore changes selection as well as weight. Under a common evidence law, more exposure makes an advocate speak less often and more extremely while moving the decision in its preferred direction. In large pools, the unique state-contingent exposure share that reproduces the complete-evidence decision balances the advocates' directional tail moments, not their observed speech. Because this share generally depends on the unknown state, we characterize the optimal ex ante compromise and solve a primitive two-state economy with a unique second-best policy. For finite pools, we derive the exact risk-minimizing adjustment, separating selection-induced cutoff bias, the receiver's fixed benchmark, and sampling variance. The attention-to-cutoff feedback survives partial weighting of empty slots and vanishes at full imputation. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.27903 |
| By: | Matthew O. Jackson; Benjamin S. Manning; Yutong Xie; Walter Yuan; Qiaozhu Mei |
| Abstract: | We introduce a general, easy-to-implement AI-based method for studying the structure and complexity of human behavior. We assign a large language model a ``type vector'' and then prompt it to choose actions across settings in which we observe human choices. For instance, the type vector (2, 4) becomes ``You are a player characterized by the following profile: 2 out of 5 in Altruism, 4 out of 5 in Risk Aversion, '' after which it is prompted to make choices. We vary the dimensions (e.g., Altruism, Fairness, Trust, $\dots$) and values (e.g., 1--5) to minimize distance to human choices. Applying the method to 119, 147 decisions made by 78, 657 subjects from more than 35 countries across 10 classic economic game roles, we find that human behavior can be closely matched using three dimensions: Risk Aversion, Strategic Sophistication, and Trust. Moreover, the types needed to fit individuals across games cluster into fewer than a dozen groups, and can predict behavior in held-out games with different rules and available actions. The results suggest that behavior across diverse settings can be approximated by a low-dimensional, portable representation, supporting the possibility of general yet parsimonious theories across the behavioral sciences. More broadly, the method can provide insights into the structure of many human behaviors. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.18265 |
| By: | Cabon-Dhersin, Marie-Laure; Poyago-Theotoky, Joanna; Raffin, Natacha |
| Abstract: | We explore the interplay of competition and environmental policies to address the question of whether green antitrust has beneficial effects in terms of both environmental and consumer welfare performance. We focus on two environmental policy tools, an emission tax and an emission standard, and explore three particular configurations: competitive ‘green R&D, collaborative ‘green’ R&D in the form of a joint lab, and the benchmark case of no ‘green’ R&D. Firms compete in the product market by selling a homogeneous product, either by setting prices (Bertrand competition) or quantities (Cournot competition) while facing convex costs. We show that ‘green antitrust’ can unambiguously improve the effectiveness of environmental policy without undermining the interests of either consumers or producers, establishing a ‘win-win-win’ outcome. |
| Keywords: | Environmental Economics and Policy, Sustainability |
| Date: | 2026–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:ags:feemwp:410235 |
| By: | Banerjee, Anwesha; Barbieri, Stefano; Konrad, Kai A. |
| Abstract: | Global systematic economic shocks may affect the Nash equilibrium contributions to international climate mitigation. We study how this effect depends on the flexibility countries have to adjust to these shocks. The kind of rigidities countries face because of technological irreversibilities plays a crucial role. Under the plausible assumption of “prudence, †higher global uncertainty tends to reduce equilibrium climate contributions if irreversibilities in the level of climate policy choices exist. And, if countries are committed to allocating a proportion of income to climate protection, rigidities may increase welfare. Thus, exercising the option to perfectly adjust one’s contributions to shocks may be another form of free riding. |
| Keywords: | Global warming; Climate Protection |
| JEL: | Q54 H41 Q55 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19283 |
| By: | Aman Ray; Srikanth Pai |
| Abstract: | In the standard Downsian model, two office-seeking parties converge to the median voter. However alienated voters may abstain and turn out only for a party within their tolerance radius. For single-peaked voter distributions, convergence survives but relocates to a central voter, the median of the electorate that participates at the convergent platform. However single-peakedness of the voter distribution is an empirically contested assumption. So we first characterize pure-strategy equilibrium for any continuous voter distribution. For general distributions, pure-strategy equilibrium can fail to exist or be non-unique, and existence of equilibrium need not persist as the tolerance radius of the voters increases. In order to resolve these issues, we propose a fundamental object: \emph{centripetal} structure for which there is a single anchor platform toward which competition always pulls. We show this structure produces convergence at equilibrium under alienation based abstention. Our main result concerns the emergence and persistence of this new structure as the tolerance radius increases. Even though equilibria for office-seeking parties themselves can vanish and reappear as the radius grows, once centripetal structure emerges, it persists as long as the midpoint voter is not alienated. Moreover, the centripetal structure always emerges, and this structure classifies equilibrium completely when parties are policy motivated. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.03788 |
| By: | Livia Ower; Edgar J. Sanchez Carrera |
| Abstract: | This paper studies why some economies remain trapped in low education and low income despite sustained social spending, and why the policy mix matters for escaping the trap. We propose a policy synergy framework in which human-capital accumulation depends on the interaction between (i) a broad universal income floor, $\tau_{univ}$, and (ii) schooling-contingent incentives, summarized by an effective conditionality multiplier $\tau_{cond}$. To this aim, we study a two-dimensional nonlinear dynamic system: an evolutionary (replicator) dynamic for the share of households investing in education, and a logistic ``income-potential'' dynamic featuring a transitional productivity valley (a J-curve) at low education shares. The model yields multiple steady states and identifies conditions under which a \emph{saddle-node bifurcation} eliminates the low-education equilibrium. A key result is that universal floors and conditional incentives are \emph{complements}: raising $\tau_{univ}$ alone may be insufficient to change long-run education when opportunity costs are high, while strong conditionality without adequate liquidity can be brittle for the poorest households. |
| Keywords: | Bifurcation Analysis; Conditional Cash Transfers; Education and Income; Evolutionary Dynamics; Poverty Traps; Universal Transfers |
| JEL: | C72 C73 I38 O15 O40 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:frz:wpaper:wp2026_12.rdf |