Exhibit 10.2

COMMON STOCK PURCHASE AGREEMENT

This Common Stock Purchase Agreement (this “Agreement”) is made and entered into as of June 30, 2015 (the “Effective Date”), by and between Capnia, Inc., a Delaware corporation with offices at 3 Twin Dolphin Drive, Suite 160, Redwood City, CA 94065 (the “Company”), and George Tidmarsh, MD, PhD, an individual with offices at [PRIVATE ADDRESS] (the “Purchaser”).

RECITALS

A. Concurrently herewith, the Company and the Purchaser are entering into the Agreement and First Amendment to Asset Purchase Agreement, dated as of even date herewith (the “Agreement and Amendment”), pursuant to which, among other things, the Asset Purchase Agreement dated May 11, 2010 between the Company and BioMedical Drug Development Inc. (“BDDI”), as transferred by BDDI to the Purchaser, will be amended upon the terms set forth therein.

B. Upon the Effective Date, the Company wishes to issue to the Purchaser 40,000 fully paid and non-assessable shares of the Company’s common stock (“Common Stock”) as consideration for the Purchaser’s entering into of the Agreement and Amendment.

AGREEMENT

In consideration of the mutual promises and covenants set forth herein, and other consideration, the receipt and adequacy of which is hereby acknowledged, the parties hereto agree as follows:

1. Issuance of Stock. The Company hereby agrees to sell and issue to the Purchaser 40,000 shares of the Company’s fully paid and non-assessable Common Stock (the “Shares”), and the Purchaser hereby agrees to purchase the Shares. The Purchaser has fully paid the purchase price for the Shares by entering into the Agreement and Amendment and consummating the transactions contemplated thereunder.

2. Form of Payment; Delivery of Stock Certificate. The consideration for the Shares shall be paid by, and effective upon, the Effective Date. As soon as practicable following the Effective Date, the Company will issue and deliver to Purchaser a certificate representing the Shares.

3. Legends. The share certificate evidencing the Shares issued hereunder shall be endorsed with the following legends:

(a) “THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR INVESTMENT AND NOT WITH A VIEW TO, OR IN CONNECTION WITH, THE SALE OR DISTRIBUTION THEREOF. NO SUCH SALE OR DISPOSITION MAY BE EFFECTED WITHOUT AN EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF 1933, AS AMENDED.”

(b) Any legend required to be placed thereon by applicable state securities laws or consistent with the Purchaser’s obligations under this Agreement.

4. Representations and Warranties of Purchaser. In connection with the purchase of the Shares, the Purchaser represents to the Company the following:

(a) The Purchaser is aware of the Company’s business affairs and financial condition and has acquired sufficient information about the Company to reach an informed and knowledgeable decision to acquire the Shares. The Purchaser is purchasing the Shares for investment for the Purchaser’s own account only and not with a view to, or for resale in connection with, any “distribution” thereof within the meaning of the Securities Act of 1933, as amended (the “Securities Act”). The Purchaser is an accredited investor within the meaning of Rule 501(a) of the Securities Act.

(b) The Purchaser understands that the Shares have not been registered under the Securities Act by reason of a specific exemption therefrom, which exemption depends upon, among other things, the bona fide nature of the Purchaser’s investment intent as expressed herein. In this connection, the Purchaser understands that, in the view of the Securities and Exchange Commission (the “Commission”), the statutory basis for such exemption may not be present if the Purchaser’s representations meant that the Purchaser’s present intention was to hold the Shares for a minimum capital gains period under the tax statutes, for a deferred sale, for a market rise, for a sale if the market does not rise or for a year or any other fixed period in the future.

(c) The Purchaser further acknowledges and understands that the Shares must be held indefinitely unless they are subsequently registered under the Securities Act or an exemption from such registration is available. The Purchaser further acknowledges and understands that the Company is under no obligation to register the Shares. The Purchaser understands that the certificate evidencing the Shares will be imprinted with a legend which prohibits the transfer of the Shares unless they are registered or such registration is not required in the opinion of counsel for the Company.

(d) The Purchaser is aware of the adoption of Rule 144 by the Commission, promulgated under the Securities Act, which permits limited public resale of securities acquired in a non-public offering subject to the satisfaction of certain conditions.

(e) The Purchaser further acknowledges that, in the event all of the requirements of Rule 144 are not met, compliance with Regulation A or some other registration exemption will be required, and that, although Rule 144 is not exclusive, the staff of the Commission has expressed its opinion that persons proposing to sell private placement securities other than in a registered offering and other than pursuant to Rule 144 will have a substantial burden of proof in establishing that an exemption from registration is available for such offers or sales and that such persons and the brokers who participate in the transactions do so at their own risk.

5. Adjustment for Stock Split. All references to the number of Shares and the purchase price of the Shares in this Agreement shall be appropriately adjusted to reflect any stock split, stock dividend or other change in the Shares which may be made by the Company after the date of this Agreement.

6. Tax Consequences. The Purchaser has reviewed with its own tax advisors the U.S. federal, state, local and foreign tax consequences of the transactions contemplated by this Agreement. With respect to such matters, the Purchaser relies solely on such advisors and not on any statements or representations of the Company or any of its agents, written or oral. The Purchaser understands that it (and not the Company) shall be responsible for its own tax liability that may arise as a result of the transactions contemplated by this Agreement.

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7. Miscellaneous.

(a) Amendment; Waiver. Except as expressly provided herein, neither this Agreement nor any term hereof may be amended, waived, discharged or terminated other than by a written instrument referencing this Agreement and signed by the Company and the Purchaser.

(b) Notices, etc. All notices and other communications required or permitted hereunder shall be in writing and shall be mailed by registered or certified mail, postage prepaid, sent by facsimile or electronic mail or otherwise delivered by hand or by messenger addressed:

(i) if to the Purchaser, at the Purchaser’s address, facsimile number or electronic mail address as shown in the Company’s records, as may be updated in accordance with the provisions hereof; or

(ii) if to the Company, to its address or facsimile number listed on the signature page of this Agreement (Attn: Chief Executive Officer), or to such other address or facsimile number as the Company shall have furnished to the Purchaser, with a copy (which shall not constitute notice under any circumstances) to Elton Satusky, Wilson Sonsini Goodrich & Rosati, 650 Page Mill Road, Palo Alto, California 94304 or at facsimile number (650) 493-6811 or at esatusky@wsgr.com.

With respect to any notice given by the Company hereunder, the Purchaser agrees that such notice may be given by facsimile or by electronic mail.

Each such notice or other communication shall for all purposes of this Agreement be treated as effective or having been given when delivered if delivered personally, or, if sent by mail, at the earlier of its receipt or 72 hours after the same has been deposited in a regularly maintained receptacle for the deposit of the United States mail, addressed and mailed as aforesaid, or, if sent by facsimile, upon confirmation of facsimile transfer, or, if sent by electronic mail, upon confirmation of delivery.

(c) Governing Law. This Agreement shall be governed in all respects by the internal laws of the State of California as applied to agreements entered into among California residents to be performed entirely within California, without regard to principles of conflicts of law.

(d) Assignment. This Agreement, and any and all rights, duties and obligations hereunder, shall not be assigned, transferred, delegated or sublicensed by the Purchaser without the prior written consent of the Company. Any attempt by the Purchaser without such permission to assign, transfer, delegate or sublicense any rights, duties or obligations that arise under this Agreement shall be void. Subject to the foregoing and except as otherwise provided herein, the provisions of this Agreement shall inure to the benefit of, and be binding upon, the successors, assigns, heirs, executors and administrators of the parties hereto.

(e) Entire Agreement. This Agreement constitutes the full and entire understanding and agreement among the parties with regard to the subjects hereof. No party shall be liable or bound to any other party in any manner with regard to the subjects hereof by any warranties, representations or covenants except as specifically set forth herein.

(f) Delay; Omission. Except as expressly provided herein, no delay or omission to exercise any right, power or remedy accruing to any party to this Agreement upon any breach or default of any other party under this Agreement shall impair any such right, power or remedy of such non-defaulting party, nor shall it be construed to be a waiver of any such breach or default, or an acquiescence therein, or of or in any similar breach or default thereafter occurring, nor shall any waiver of any single breach or default be deemed a waiver of any other breach or default theretofore or thereafter occurring. Any waiver, permit, consent or

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approval of any kind or character on the part of any party of any breach or default under this Agreement, or any waiver on the part of any party of any provisions or conditions of this Agreement, must be in writing and shall be effective only to the extent specifically set forth in such writing. All remedies, either under this Agreement or by law or otherwise afforded to any party to this Agreement, shall be cumulative and not alternative.

(g) Severability. If any provision of this Agreement becomes or is declared by a court of competent jurisdiction to be illegal, unenforceable or void, portions of such provision, or such provision in its entirety, to the extent necessary, shall be severed from this Agreement, and such court will replace such illegal, void or unenforceable provision of this Agreement with a valid and enforceable provision that will achieve, to the extent possible, the same economic, business and other purposes of the illegal, void or unenforceable provision. The balance of this Agreement shall be enforceable in accordance with its terms.

(h) Counterparts. This Agreement may be executed in any number of counterparts, each of which shall be enforceable against the parties actually executing such counterparts, and all of which together shall constitute one instrument.

(i) Jurisdiction; Venue. With respect to any disputes arising out of or related to this Agreement, the parties consent to the exclusive jurisdiction of, and venue in, the state courts in San Mateo County in the State of California (or, in the event of exclusive federal jurisdiction, the courts of the Northern District of California).

(j) Further Assurances. Each party hereto agrees to execute and deliver, by the proper exercise of its corporate, limited liability company, partnership or other powers, all such other and additional instruments and documents and do all such other acts and things as may be necessary to more fully effectuate this Agreement.

[Remainder of Page Intentionally Left Blank]

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IN WITNESS WHEREOF, the parties have duly executed this Agreement as of the Effective Date.

[Signature Page to Capnia, Inc. Common Stock Purchase Agreement]