Luis R. Izquierdo

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Learning and Evolutionary Game Theory

Positive and negative selective assortment
Izquierdo, S.S. & Izquierdo, L.R. & Hauert, C. (2025). Journal of Theoretical Biology, vol. 608, 112129.
[Download] | [Software]
Strategy sets closed under payoff sampling
Izquierdo, S.S. & Izquierdo, L.R. (2023). Games and Economic Behavior, vol. 138, pp. 126-142.
[Download at publishers's site] | [Download] | [Software 1 (EvoDyn-3s)] | [Software 2 (BEP-3s-sp)]
Stability of Strict Equilibria in Best Experienced Payoff Dynamics: Simple Formulas and Applications
Izquierdo, S.S. & Izquierdo, L.R. (2022) Journal of Economic Theory, 206, 105553.
[Download] | [Software 1 (EvoDyn-3s)] | [Software 2 (BEP-TCG)]
Fast and Scalable Global Convergence in Single-Optimum Decentralized Coordination Problems
Izquierdo, L.R. & Izquierdo, S.S. & Rodríguez, J. (2022). IEEE Transactions on Control of Network Systems, vol. 9, issue 4, pp. 1937-1948.
[Download at publishers's site] | [Download] | [Presentation]
[Agent-based model nBEPA1 in SOC games] | [Agent-based model nBEPA1 in SOC games played in networks]
“Test two, choose the better" leads to high cooperation in the Centipede game
Izquierdo, S.S. & Izquierdo, L.R. (2022). Journal of Dynamics and Games, vol. 9, issue 4, pp. 461-498.
[Download at publishers's site] | [Working Paper] | [Agent-based model] | [Mathematica notebook]
Stability for Best Experienced Payoff Dynamics
Sandholm, W.H., Izquierdo, S.S. & Izquierdo, L.R. (2020) Journal of Economic Theory, 185, 104957.
[Download at publishers's site] | [Working Paper] | [Mathematica program]
Best Experienced Payoff Dynamics and Cooperation in the Centipede Game
Sandholm, W.H., Izquierdo, S.S. & Izquierdo, L.R. (2019). Theoretical Economics 14, pp. 1347–1385.
[Download] | [Online appendix] | [Mathematica notebook]
An Introduction to ABED: Agent-Based Simulation of Evolutionary Game Dynamics
Izquierdo, L.R., Izquierdo, S.S. & Sandholm, W.H. (2019). Games and Economic Behavior, 118, pp. 434-462.
[Download at publishers's site] | [Working Paper] | [Online appendix] | [abed-1pop] | [abed-2pop] | [Presentation]
EvoDyn-3s: A Mathematica Computable Document to Analyze Evolutionary Dynamics in 3-Strategy Games
Izquierdo, L.R., Izquierdo, S.S. & Sandholm, W.H. (2018). SoftwareX, 7, pp. 226-233.
[Download] | [Software]
Mixing and diffusion in a two-type population
Izquierdo, S.S., Izquierdo, L.R. & López-Pintado, D. (2018). Royal Society Open Science, 5(2) 172102.
[Download] | [NetLogo model] | [Mathematica demonstration] | [Presentation] | [Video (Spanish)]
Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation
Izquierdo, L.R., Izquierdo, S.S. & Vega-Redondo, F. (2014). Journal of Economic Dynamics & Control 46, pp. 91-113.
[Download at publishers's site] | [Download unformatted version] | [Computational model] | [Presentation]
7-page introduction to classical, learning, and evolutionary game theory. [Download] | [Download at publisher]
Izquierdo, L.R., Izquierdo, S.S. & Vega-Redondo, F. (2012). In N. M. Seel (Ed.) Encyclopedia of the Sciences of Learning, Part 12, pp. 1782-1788. ISBN: 978-1-4419-1427-9. New York: Springer.
4-page introduction to reinforcement learning. [Download] | [Download at publisher]
Izquierdo, L.R. & Izquierdo, S.S. (2012). In N. M. Seel (Ed.) Encyclopedia of the Sciences of Learning, Part 18, pp. 2796-2799. ISBN: 978-1-4419-1427-9. New York: Springer.
Strictly Dominated Strategies in the Replicator-Mutator Dynamics [Download]
Izquierdo, S.S. & Izquierdo, L.R. (2011). Games, Volume 2, Issue 3, pp. 355-364.
[Model (The replicator-mutator dynamics with 3 strategies)]
The Option to Leave: Conditional Dissociation in the Evolution of Cooperation [Download]
Izquierdo, S.S., Izquierdo, L.R. & Vega-Redondo, F. (2010). Journal of Theoretical Biology, Volume 267, Issue 1, pp. 76-84.
[Unformatted version] | [Supplementary material] | [Model (with constant population)] | [Model (with fluctuating population)] | [Presentation]
Reinforcement Learning Dynamics in Social Dilemmas. [Download]
Izquierdo, S.S., Izquierdo, L.R. and Gotts, N.M. (2008). Journal of Artificial Societies and Social Simulation 11(2)1.
[Model] | [Expected motion]
Dynamics of the Bush-Mosteller Learning Algorithm in 2x2 Games. [Download]
Izquierdo, L.R. and Izquierdo, S.S. (2008). Chapter 11 in Reinforcement Learning. Theory and Applications, edited by Cornelius Weber, Mark Elshaw and Norbert Michael Mayer. I-Tech Education and Publishing, Vienna, Austria. ISBN 978-3-902613-14-1.
Advancing Learning and Evolutionary Game Theory with an Application to Social Dilemmas. [Details and Download]
Izquierdo, L.R. (2008). PhD Thesis.
Transient and asymptotic dynamics of reinforcement learning in games. [Download]
Izquierdo, L.R., Izquierdo, S.S., Gotts, N.M. & Polhill, J.G. (2007). Games and Economic Behavior, Volume 61, Issue 2, pp. 259-276.
[Model] | [Expected motion] | [Presentation]
On the structural robustness of evolutionary models of cooperation.
Izquierdo, S.S. and Izquierdo, L.R. (2006). Lecture Notes in Computer Science 4224, pp. 172-182.
[Download] | [Poster] | [Download at publisher]
The implications of case-based reasoning in strategic contexts.
Izquierdo, L.R. and Gotts, N.M. (2006). Lecture Notes in Economics and Mathematical Systems 564, pp. 163-174.
[Download] | [Poster] | [Download at publisher]
Appearances can be deceiving: lessons learned reimplementing Axelrod's "evolutionary approach to norms".
Galan, J.M. and Izquierdo, L.R. (2005). Journal of Artificial Societies and Social Simulation 8(3)2.
[Download] | [Presentation]
Case-based reasoning, social dilemmas, and a new equilibrium concept. [Download]
Izquierdo, L.R., Gotts, N.M. and Polhill, J.G. (2004). Journal of Artificial Societies and Social Simulation 7(3)1. [Poster]

More general Economics

Empowering Energy Communities: Three Methods to Distribute Savings in Local Energy Markets
Gonzalez-Asenjo, D., Izquierdo, L.R. & Sedano, J. (2024). DYNA, vol. 99(4), pp. 417-423. DOI: 10.52152/D11065
[Download at publishers's site]
A simple and efficient method to allocate costs and benefits in energy communities
Gonzalez-Asenjo, D., Izquierdo, L.R. & Sedano, J. (2023). Journal of Industrial Engineering and Management, vol. 16(2), pp. 398-424. DOI: 10.3926/jiem.5514
[Download at publishers's site]
The economics of utopia: a co-evolutionary model of ideas, citizenship and socio-political change. [Download]
Almudí, I., Fatás-Villafranca, F., Izquierdo, L.R. & Jason Potts (2017). Journal of Evolutionary Economics, 27(4), 629-662.
[Download at Publisher's website] | [Model]
Economía Artificial: una valoración crítica [Download]
Izquierdo, S.S., Izquierdo, L.R., Galán J.M. & Santos, J.I. (2016). Revista de Métodos Cuantitativos para la Economía y la Empresa, vol. 22, pp. 36-54. [es]
The "Win-Continue, Lose-Reverse" Rule in Oligopolies: Robustness of Collusive Outcomes [Download]
Izquierdo, S.S. & Izquierdo, L.R. (2015). Advances in Complex Systems, vol. 18, nos. 5 & 6, 1550013.
[Download at Publisher's website] | [Cournot Model] | [Bertrand Model]
The "Win-Continue, Lose-Reverse" Rule in Cournot Oligopolies: Robustness of Collusive Outcomes [Download]
Izquierdo, S.S. & Izquierdo, L.R. (2015). In Amblard, F., Miguel, F.J., Blanchet, A., Gaudou, B. (Eds.) Advances in Artificial Economics, Lecture Notes in Economics and Mathematical Systems, Vol. 676, pp 33-44.
[Download at Publisher's website] | [Model]
Industry dynamics, technological regimes and the role of demand. [Download]
Almudí, I., Fatás-Villafranca, F. & Izquierdo, L.R. (2013). Journal of Evolutionary Economics Vol. 23, Issue 5, pp 1073-1098.
[Download at Publisher's website] | [Model]
Branching innovation, recombinant innovation, and endogenous technological transitions. [Download]
Frenken, K., Izquierdo, L.R. & Zeppini,P. (2012). Environmental Innovation and Societal Transitions, Volume 4, pp. 25-35.
[Download at Publisher's website] | [Model]
Innovation, Catch-up and Leadership in Science-Based Industries. [Download]
Almudí, I., Fatás-Villafranca, F. & Izquierdo, L.R. (2012). Industrial and Corporate Change, Volume 21, Number 2, pp. 345-375.
[Unformatted version] | [Model]
Modeling endogenous rule changes in an institutional context: the ADICO sequence. [Download]
Smajgl, A., Izquierdo, L.R. and Huigen, M. (2008). Advances in Complex Systems, Volume 11, Issue 2, pp. 199-215.
The impact of quality uncertainty without asymmetric information on market efficiency. [Download]
Izquierdo, S.S. and Izquierdo, L.R. (2007). Journal of Business Research, Volume 60, Issue 8, pp. 858-867.
[Model] [Download at Publisher's website]
Market failure caused by quality uncertainty. [Download]
Izquierdo, S.S., Izquierdo, L.R., Galán, J.M. and Hernández, C. (2006). Lecture Notes in Economics and Mathematical Systems 564, pp. 203-213.

Networks

Research impact within the international arid literature: An Australian perspective based on network theory. [Download]
McAllister, R.R.J., Izquierdo, L.R., Janssen, M.A. and Stafford Smith, D.M. (2009). Journal of Arid Environments, Volume 73, Issue 9, pp. 862-871.
Introduction to the Formal Analysis of Social Networks Using Mathematica. (Version 2)
Izquierdo, L.R. and Hanneman, R.A. (2006). Published in digital form at http://luis.izqui.org. Burgos, Spain.
[Document (.pdf)] | [Mathematica notebook (.nb)] | [Mathematica Player]

Computer (mostly agent-based) modelling

Social simulation models as refuting machines
Mauhe, N., Izquierdo, L.R. & Izquierdo, S.S. (2023). Journal of Artificial Societies and Social Simulation 26(2)8. DOI: 10.18564/jasss.5076
[Download] | [Download PDF] | [Software]
Mamdani Fuzzy Systems for Modelling and Simulation: A Critical Assessment
Izquierdo S.S. & Izquierdo, L.R. (2018). Journal of Artificial Societies and Social Simulation 21(3)2. DOI: 10.18564/jasss.3660
[Download]
Fuzzy Logic for Social Simulation using NetLogo
Izquierdo, L.R., Olaru, D., Izquierdo S.S., Purchase, S. & Soutar, G.N. (2015). Journal of Artificial Societies and Social Simulation 18(4)1. DOI: 10.18564/jasss.2885
[Download] | [Extension, source code, user guide, cheat sheet, and a sample model with a tutorial] | [Blog post]
Combining Mathematical and Simulation Approaches to Understand the Dynamics of Computer Models. [Download] | [Download at publisher]
Izquierdo, L.R., Izquierdo, S.S., Galán, J.M. & Santos, J.I. (2013). In Edmonds, B. & Meyer, R. (eds.) Simulating Social Complexity: A Handbook. Series: Understanding Complex Systems. Springer-Verlag, pp. 235-271.
Checking Simulations: Detecting and Avoiding Errors and Artefacts. [Download] | [Download at publisher]
Galán, J.M., Izquierdo, L.R., Izquierdo, S.S., Santos, J.I., del Olmo, R. & López-Paredes (2013). In Edmonds, B. & Meyer, R. (eds.) Simulating Social Complexity: A Handbook. Series: Understanding Complex Systems. Springer-Verlag, pp. 95-116.
Stochastic Approximation to Understand Simple Simulation Models. [Download] | [Download at publisher]
Izquierdo, S.S. & Izquierdo, L.R. (2013). Journal of Statistical Physics, 151 (1) pp. 254-276.
[Model]
Techniques to Understand Computer Simulations: Markov Chain Analysis. [Download]
Izquierdo, L.R., Izquierdo, S.S., Galán J.M. & Santos, J.I. (2009). Journal of Artificial Societies and Social Simulation 12(1)6.
[ Document + models (.zip)]
Errors and artefacts in agent-based modelling. [Download]
Galán J.M., Izquierdo, L.R., Izquierdo, S.S., Santos, J.I., Olmo, R., López-Paredes, A. & Edmonds, B. (2009). Journal of Artificial Societies and Social Simulation 12(1)1.
Modelado de sistemas complejos mediante simulación basada en agentes y mediante dinámica de sistemas. [Download]
Izquierdo, L.R., Galán J.M., Santos, J.I. and Olmo, R. (2008). Empiria 16, pp. 85-112. [es]

The Impact of Floating-point Errors on Agent-based Models

Is your model susceptible to floating-point errors?. [Download]
Izquierdo, L.R. and Polhill, J.G. (2006). Journal of Artificial Societies and Social Simulation 9(4)4.
What every agent-based modeller should know about floating point arithmetic. [Download]
Polhill, J.G., Izquierdo, L.R. and Gotts, N.M. (2006). Environmental Modelling & Software, 21 (3), March 2006. pp. 283-309.
Lessons learned from converting the Artificial Stock Market to interval arithmetic. [Download]
Polhill, J.G. and Izquierdo, L.R. (2005). Journal of Artificial Societies and Social Simulation 8(2)2.
The ghost in the model (and other effects of floating point arithmetic). [Download]
Polhill, J.G., Izquierdo, L.R. and Gotts, N.M. (2005). Journal of Artificial Societies and Social Simulation 8(1)5.

Others

Book Review of "Complexity: A Guided Tour. Melanie Mitchell (2009)". [Download] | [Unformatted version]
Izquierdo, L.R. (2010). Artificial Life, Vol. 16, No. 3, pp. 259-264.
Publishing science in the digital age. The case of Neurocirugía. [English] | [Spanish]
Izquierdo, S.S., Izquierdo, L.R. and Izquierdo, J.M. (2007). Neurocirugía, Volume 18, Issue 3, pp. 193-200.