{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4MIMULGQ6NYIMD46KDG2EA77OC","short_pith_number":"pith:4MIMULGQ","canonical_record":{"source":{"id":"1506.04698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-06-15T18:46:41Z","cross_cats_sorted":["math.OC","math.PR"],"title_canon_sha256":"baf8c8abbf7af56dd0f2f67174b02249246f0ad8f256c7b40c21b6916c83fbaa","abstract_canon_sha256":"08a84e9ae950948e1f906d18382dd1887b3037087efa359add880582c25b5edb"},"schema_version":"1.0"},"canonical_sha256":"e310ca2cd0f370860f9e50cda203ff7091e19858ec37ef2ef9b296d46a38dc19","source":{"kind":"arxiv","id":"1506.04698","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04698","created_at":"2026-05-18T01:49:25Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04698v1","created_at":"2026-05-18T01:49:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04698","created_at":"2026-05-18T01:49:25Z"},{"alias_kind":"pith_short_12","alias_value":"4MIMULGQ6NYI","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MIMULGQ6NYIMD46","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MIMULGQ","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4MIMULGQ6NYIMD46KDG2EA77OC","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-06-15T18:46:41Z","cross_cats_sorted":["math.OC","math.PR"],"title_canon_sha256":"baf8c8abbf7af56dd0f2f67174b02249246f0ad8f256c7b40c21b6916c83fbaa","abstract_canon_sha256":"08a84e9ae950948e1f906d18382dd1887b3037087efa359add880582c25b5edb"},"schema_version":"1.0"},"canonical_sha256":"e310ca2cd0f370860f9e50cda203ff7091e19858ec37ef2ef9b296d46a38dc19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:25.140160Z","signature_b64":"HvJMhXZBdRCi9UAzY69ys1oREfUEDEyTi1GNHEgEsHysQWrXPO3ADLIUQMZioG9Ss5Pxr4cheoq46IqeQDfGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e310ca2cd0f370860f9e50cda203ff7091e19858ec37ef2ef9b296d46a38dc19","last_reissued_at":"2026-05-18T01:49:25.139276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:25.139276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04698","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDDsCOEkY1yoJY7U4WYl5nGK4Y25+HQMZyJJG6pOOg/+JfK5eqyS+dfyhxEQJXhbwQyv0mXdDzNqrsabHsylDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:56:30.210841Z"},"content_sha256":"afbd139e839075ea24ef83c99216fa3d5ac9b30a80bebcaa72c4f0eddeaabe37","schema_version":"1.0","event_id":"sha256:afbd139e839075ea24ef83c99216fa3d5ac9b30a80bebcaa72c4f0eddeaabe37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4MIMULGQ6NYIMD46KDG2EA77OC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quick or Persistent? Strategic Investment Demanding Versatility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.PR"],"primary_cat":"q-fin.EC","authors_text":"Jacco Thijssen, Jan-Henrik Steg","submitted_at":"2015-06-15T18:46:41Z","abstract_excerpt":"In this paper we analyse a dynamic model of investment under uncertainty in a duopoly, in which each firm has an option to switch from the present market to a new market. We construct a subgame perfect equilibrium in mixed strategies and show that both preemption and attrition can occur along typical equilibrium paths. In order to determine the attrition region a two-dimensional constrained optimal stopping problem needs to be solved, for which we characterize the non-trivial stopping boundary in the state space. We explicitly determine Markovian equilibrium stopping rates in the attrition reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04698","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eBUdFWFxq5uQTkl/3ufWe9dBlGZwBtpUN7MKPTH9At//5dRdUPdOlCsqodv9z6WimhlcbVR9pmv5J/vMCblIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:56:30.211192Z"},"content_sha256":"8e915bff77c0f8398b83290e4dbd07ef8b0b095c16958e36b60c5e825d631fac","schema_version":"1.0","event_id":"sha256:8e915bff77c0f8398b83290e4dbd07ef8b0b095c16958e36b60c5e825d631fac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MIMULGQ6NYIMD46KDG2EA77OC/bundle.json","state_url":"https://pith.science/pith/4MIMULGQ6NYIMD46KDG2EA77OC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MIMULGQ6NYIMD46KDG2EA77OC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T17:56:30Z","links":{"resolver":"https://pith.science/pith/4MIMULGQ6NYIMD46KDG2EA77OC","bundle":"https://pith.science/pith/4MIMULGQ6NYIMD46KDG2EA77OC/bundle.json","state":"https://pith.science/pith/4MIMULGQ6NYIMD46KDG2EA77OC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MIMULGQ6NYIMD46KDG2EA77OC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4MIMULGQ6NYIMD46KDG2EA77OC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"08a84e9ae950948e1f906d18382dd1887b3037087efa359add880582c25b5edb","cross_cats_sorted":["math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-06-15T18:46:41Z","title_canon_sha256":"baf8c8abbf7af56dd0f2f67174b02249246f0ad8f256c7b40c21b6916c83fbaa"},"schema_version":"1.0","source":{"id":"1506.04698","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04698","created_at":"2026-05-18T01:49:25Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04698v1","created_at":"2026-05-18T01:49:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04698","created_at":"2026-05-18T01:49:25Z"},{"alias_kind":"pith_short_12","alias_value":"4MIMULGQ6NYI","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MIMULGQ6NYIMD46","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MIMULGQ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:8e915bff77c0f8398b83290e4dbd07ef8b0b095c16958e36b60c5e825d631fac","target":"graph","created_at":"2026-05-18T01:49:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we analyse a dynamic model of investment under uncertainty in a duopoly, in which each firm has an option to switch from the present market to a new market. We construct a subgame perfect equilibrium in mixed strategies and show that both preemption and attrition can occur along typical equilibrium paths. In order to determine the attrition region a two-dimensional constrained optimal stopping problem needs to be solved, for which we characterize the non-trivial stopping boundary in the state space. We explicitly determine Markovian equilibrium stopping rates in the attrition reg","authors_text":"Jacco Thijssen, Jan-Henrik Steg","cross_cats":["math.OC","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-06-15T18:46:41Z","title":"Quick or Persistent? Strategic Investment Demanding Versatility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04698","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:afbd139e839075ea24ef83c99216fa3d5ac9b30a80bebcaa72c4f0eddeaabe37","target":"record","created_at":"2026-05-18T01:49:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"08a84e9ae950948e1f906d18382dd1887b3037087efa359add880582c25b5edb","cross_cats_sorted":["math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-06-15T18:46:41Z","title_canon_sha256":"baf8c8abbf7af56dd0f2f67174b02249246f0ad8f256c7b40c21b6916c83fbaa"},"schema_version":"1.0","source":{"id":"1506.04698","kind":"arxiv","version":1}},"canonical_sha256":"e310ca2cd0f370860f9e50cda203ff7091e19858ec37ef2ef9b296d46a38dc19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e310ca2cd0f370860f9e50cda203ff7091e19858ec37ef2ef9b296d46a38dc19","first_computed_at":"2026-05-18T01:49:25.139276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:25.139276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HvJMhXZBdRCi9UAzY69ys1oREfUEDEyTi1GNHEgEsHysQWrXPO3ADLIUQMZioG9Ss5Pxr4cheoq46IqeQDfGAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:25.140160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04698","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afbd139e839075ea24ef83c99216fa3d5ac9b30a80bebcaa72c4f0eddeaabe37","sha256:8e915bff77c0f8398b83290e4dbd07ef8b0b095c16958e36b60c5e825d631fac"],"state_sha256":"f7902994fe76526c4bb3e6f58d005ec387da89193dddecb510060e632c3e39b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HpU/xP4ZtW5Ov+w5lMZn60ew7v5qus2oKrcN3zqgdzH2549O6zxO3OTtN2V5Ky9mD6BvEFYqT9/DSh7YuUwIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:56:30.213108Z","bundle_sha256":"f6bc9b1cc11b2af44038117074ac953f0af267e4b525d376189dc4f7563243cf"}}