{ "_id": "6a1ee1b0b401979e73410ab2", "Package": "GNE", "Type": "Package", "Title": "Computation of Generalized Nash Equilibria", "Version": "0.99-7", "Authors@R": "person(\"Christophe\", \"Dutang\", role = c(\"aut\", \"cre\"),\nemail = \"dutangc@gmail.com\", comment = c(ORCID = \"0000-0001-6732-1501\"))", "Description": "Compute standard and generalized Nash Equilibria of\nnon-cooperative games. Optimization methods available are\nnonsmooth reformulation, fixed-point formulation, minimization\nproblem and constrained-equation reformulation. See e.g. Kanzow\nand Facchinei (2010), .", "License": "GPL (>= 2)", "Encoding": "UTF-8", "VignetteBuilder": "knitr", "BuildVignettes": "true", "URL": "https://r-forge.r-project.org/projects/optimizer/", "Repository": "https://r-forge.r-universe.dev", "Date/Publication": "2025-01-04 15:10:34 UTC", "RemoteUrl": "https://github.com/r-forge/optimizer", "RemoteRef": "HEAD", "RemoteSha": "67f18d75bb68f3ca85ae8b27c75bf0c06df0e0df", "RemoteSubdir": "pkg/GNE", "NeedsCompilation": "yes", "Packaged": { "Date": "2026-05-20 06:54:56 UTC", "User": "root" }, "Author": "Christophe Dutang [aut, cre] (ORCID:\n)", "Maintainer": "Christophe Dutang ", "MD5sum": "7b504396f1b55139e914a1a17a79547b", "_user": "r-forge", "_type": "src", "_file": "GNE_0.99-7.tar.gz", "_fileid": "13b7f8029633e44eb93929529ba0744b1bbbf708da24b07506b0bdad3a234424", "_filesize": 529503, "_sha256": "13b7f8029633e44eb93929529ba0744b1bbbf708da24b07506b0bdad3a234424", "_created": "2026-05-20T06:54:56.000Z", "_published": 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equation reformulation of the GNE problem.", "topics": [ "GNE.ceq" ] }, { "page": "GNE.fpeq", "title": "Fixed point equation reformulation of the GNE problem.", "topics": [ "GNE.fpeq" ] }, { "page": "GNE.minpb", "title": "Non smooth equation reformulation of the GNE problem.", "topics": [ "GNE.minpb" ] }, { "page": "GNE.nseq", "title": "Non smooth equation reformulation of the GNE problem.", "topics": [ "GNE.nseq" ] }, { "page": "util-NIR", "title": "Nikaido Isoda Reformulation", "topics": [ "fpNIR", "gapNIR", "gradxgapNIR", "gradygapNIR" ] }, { "page": "util-potentreduc", "title": "Potential reduction algorithm utility functions", "topics": [ "gradpotential.ce", "gradpsi.ce", "potential.ce", "psi.ce" ] }, { "page": "util-projection", "title": "Projection of a point on a set", "topics": [ "Projector", "projector" ] }, { "page": "util-rejectalgo", "title": "Rejection method for random generation.", "topics": [ "rejection" ] }, { "page": "util-SSR", "title": "SemiSmooth Reformulation", "topics": [ "funSSR", "jacSSR", "SSR" ] }, { "page": "util-stepfunc", "title": "Step functions", "topics": [ "decrstep", "decrstep10", "decrstep20", "decrstep5", "purestep", "stepfunc" ] }, { "page": "util-VIR", "title": "Nikaido Isoda Reformulation", "topics": [ "fpVIR", "gapVIR", "gradxgapVIR", "gradygapVIR" ] } ], "_readme": "https://github.com/r-forge/optimizer/raw/HEAD/pkg/GNE/README.md", "_rundeps": [ "alabama", "BB", "nleqslv", "numDeriv", "quadprog", "SQUAREM" ], "_vignettes": [ { "source": "GNE-optim-bench.Rmd", "filename": "GNE-optim-bench.html", "title": "Optimization benchmark with the GNE package", "author": "Christophe Dutang", "engine": "knitr::rmarkdown", "headings": [ "Introduction", "GNEP as a nonsmooth equation", "Notation and definitions", "A classic example", "Usage example", "Localization of the GNEs", "Benchmark of the complementarity functions and the computation methods", "Initial point $z_0 = (4, -4, 1, 1)$", "Initial point $z_0 = (-4, 4, 1, 1)$", "Initial point $z_0 = (3, 0, 1, 1)$", "Initial point $z_0 = (0, 3, 1, 1)$", "Initial point $z_0 = (-1, -1, 1, 1)$", "Initial point $z_0 = (0, 0, 1, 1)$", "Conclusions", "Special case of shared constraints with common multipliers", "Constrained-equation reformulation of the KKT system", "GNEP as a fixed point equation or a minimization problem", "NI reformulation", "QVI reformulation", "The jointly convex case", "In this subsection, we present reformulations for a subclass of GNEP called jointly convex case.Firstly, the jointly convex setting requires that the constraint function is common to all players $g^1=\\dots =g^N= g$.Then, we assume, there exists a closed convex subset $X \\subset \\R^n$ such that for all player $i$,$$", "NIF formulation for the jointly convex case", "QVI formulation for the jointly convex case", "List of examples", "Tables for the nonsmooth reformulation", "Appendix for the nonsmooth reformulation", "\\subsection{Semismooth reformulation -- Shared constraint case\\label{app:ceq:jointcase}}The Jacobian is given by$$\\Jac \\widetilde H(x, \\tilde \\lambda, \\tilde w) =\\left(\\begin{matrix}\\Jac_x \\bar L (x, \\tilde \\lambda) & \\Jac_{\\tilde \\lambda} \\bar L (x, \\tilde \\lambda) & 0 \\\\Jac_x \\tilde g(x) & 0 & I \\0 & \\diag[\\tilde w] & \\diag[\\tilde \\lambda]\\end{matrix}\\right),$$where$$\\Jac_{\\tilde \\lambda} \\bar L (x, \\tilde \\lambda)" ], "created": "2023-03-29 19:59:07", "modified": "2024-10-17 14:21:24", "commits": 3 } ], "_score": 5.049218022670182, "_indexed": true, "_nocasepkg": "gne", "_universes": [ "r-forge", "dutangc" ], "_binaries": [ { "r": "4.6.0", "os": "win", "version": "0.99-7", "date": "2026-04-20T05:56:25.000Z", "arch": "x86_64", "commit": "67f18d75bb68f3ca85ae8b27c75bf0c06df0e0df", "fileid": "d9aaf3f634e65719533a3eb136083e0b3b9afce0e8fb96267d26567e09b63d49", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/r-forge/actions/runs/24650695755" }, { "r": "4.7.0", "os": "linux", 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